When Odysseus made Corfu his final stop on his long journey home to Ithaca, he was plied with bread, wine, spit-roast meat and 'many little dainties'. Today's travellers, alighting from a plane at Kerkyra and driving a few kilometres up the coast might settle instead for burger and chips and a game of paint ball.

Little Corfu, the 'Emerald Isle', northernmost of the seven Ionian islands, just 70km long and 15 wide, has been settled and resettled throughout history. It has been ruled by Rome and Byzantium, by the Normans and the Angevin conquerors of southern Italy. It was for four centuries under the patronage of Venice. It passed from Republican France to a Russo-Turkish alliance, then to Imperial France. From 1814 to 1864 it was a British protectorate, before being ceded to Greece. In World War I, the French took military possession. In World War II, first the Italians then the Germans moved in. And, since the early 1960s, tourists have descended in their hordes. Every year, more than a million visitors, half of them Brits, flock to an island with a population of just 93,000.

The waves on waves of incomers have, of course, left their mark. In the capital, Corfu Town, the architecture shows Venetian, French and British influences. The colonnaded Liston building recalls the Rue de Rivoli in Paris. A cricket pitch recalls Surrey. Around the coast, night clubs and discos, Irish pubs, video bars, mini-markets and souvenir shops in hot-spots such as Kavos and Ipsos are a constant reminder of the summer revellers.

But, for all this, there is a kind of immutability in the spirit of the place, which has been anything but overrun. Avoid the tacky resorts, turn your eyes inland, and you see that Corfu is very much its own island, the Corfiots very much their own people, albeit with a taste for pasta. They cook as they speak - basically Greek, with a faint Italian accent - and it is to learn something of their cuisine that we were there.

In the village of Pythos, a slightly dizzying 80-minute coastal drive from the airport, British couple Ben Philo and Claudia Pollinger teach Corfiot cooking with a slight modern spin, offering five-day courses in May and October, for up to six people. This is a nice, intimate number, and, in the last week of October, I joined just three others - John and Jeanette, semi-retired teachers from Lincolnshire, and Jane, a British ex-pat Corfu resident with her own textile business. The mood was fun and friendly but quite focused, with 'real, hands-on cooking every day', as promised.

Ben and Claudia are from different culinary backgrounds. He trained at catering college, worked at the five-star Inn at Perry Cabin, Maryland, and spent two years at Anthony Worrall Thompson's London restaurant Wiz (where he met Claudia) before becoming sous-chef at the Accor hotel on the South Bank. She started out in publishing and film animation, spent a year in a European restaurant in Hong Kong, set up a pasta cafe in Goa, then returned to London to work for AWT at both WOZ and WIZ, before becoming head chef at Model Catering, cooking for fashion shoots and film premieres. They make a great double act, playing to each other's strengths, now and then indulging in. good-humoured tiffs before agreeing to differ, with the formula cookery is 'not an exact science'. (Tell that to Heston Blumenthal!)

Cooking holidays are a growth industry, particularly in Italy, France and Spain. You can learn to make ravioli con porri e turtufo in Tuscany, pigeon roti a l'Armagnac in Gascony, gazpacho, ajo blanco, salmorejo in Andalusia, in more opulent surroundings than these, but Corfu has its own special appeal. Still, it was a slightly quirky choice for Ben and Claudia. What decided them?

'I'd always wanted to live abroad,' said Claudia, 'and we knew someone who was building a house here, who raved about it. Ben loved Greece, but I'd never been, so we came to Corfu for a week's holiday and instantly fell in love with it. I really liked it because it reminded me of Goa. That sounds bizarre, but the villages are very similar, and the colours. Instead of palm trees there were olive trees, but there were views I felt I'd seen before. I thought Goa was absolutely the most wonderful place on earth, but Corfu is so beautiful. It has wonderful weather, it seemed well contained, very safe, and it is an island, which is sort of romantic.'

With her imagination fired by that brief holiday, Claudia emailed CV Travel and Travel A La Carte. 'I said, "We have the idea of doing private villa catering on Corfu. Do you think it's a business that might work?" And, the same day, A La Carte emailed me back, and the owner of CV rang me to say, "You must come and see me." I had really positive feedback.'

So, four years ago, they launched their enterprise, and in June 2005 they moved into new premises, a former olive press, converted to their specifications in just five months. Trading also as The Invisible Kitchen, they offer villa and event catering, wait at table or efface themselves and operate behind the scenes, according to their clients' wishes. They hold a monthly supper-club in their private dining room, for a minimum of 10 diners, and, on top of this, they have son Max, born in 2003, and baby Molly to raise. In high summer they must be run ragged, but they seem to thrive on it.

On the first morning, they had us poaching quinces in sweet Mavrodaphne wine, making a braised beef dish, 'sofrito' (from the Italian soffriggere, to fry lightly), tzatziki, a 'really useful tomato sauce', aubergine salad and baked feta - they had us taste three types of feta, from goat, sheep and cow's milk. On the second day, it was olive oil bread with rosemary, gigantes (giant beans in that really useful sauce), a walnut cake drenched in orange and Metaxa syrup, spanakopita (the ubiquitous Greek filo pastry, spinach and feta pie), and bourtheto (fish stew, from the Venetian brodetto, for soup or broth), plus some courgette and haloumi fritters, because Claudia could not resist the young, pale green and sprightly vegetables, still sporting their pretty flower hats, in the market.

At around two o'clock, we would all sit down to lunch out on the courtyard, tasting local wines with what we had prepared, then the rest of the day was our own.

Anyone from a relative novice to a competent home cook could learn here: from trade techniques, 'knife skills', charcoal-grilling, filleting, secrets of chopping garlic, how to recognise sea-fresh fish, how to handle notoriously temperamental filo pastry (and, incidentally, where to buy some excellent, sturdy, serviceable non-stick pans: Lidl, since you ask). True, you could also learn at evening classes, how to poach a quince, you could reach for a book and make a reasonable fist of sofrito. But the joy of such a course is context: the organised trips to the street market in Corfu town, to a wine-tasting in a cava; meals in the uncompromisingly authentic Rouvas taverna; dinner in a private hilltop house. And also, you know, just by being there.

Corfu town is wonderful. "We feel a pride in showing people around," said Claudia, "I don't think we'll ever get tired of it, because it's such a surprise and we love it so much." It is dominated by two forts, from the 12th and 13th centuries, boasts a museum of bank notes, and was the birthplace, on June 10, 1921, of the then Prince Philip of Greece and Denmark, Duke of Edinburgh, Earl of Merioneth and Baron Greenwich.

Rouvos, a father-and-sons venture, though a bit rough and ready, is not to be missed. Set aside the written menu and go up to the counter to check the dishes of roast meats, moussaka, rice-stuffed vegetables and pastitsio (a kind of upstanding macaroni cheese with a layer of meat filling). Go behind it to inspect the seething pans of sofrito, chick pea soup and a pungent and bristling bourtheto, which looks right back at you and is not for the faint-hearted. Be sure to have the lemon roast potatoes. Wash them down with a flask of retsina, which costs approximately nothing. The proprietors speak English, as do most of Corfu's inhabitants. The taller son is probably called Adonis.

In the daily market there is a sense of superabundance, of nature's largesse, so sadly lacking in UK street or farmer's markets. Most stalls are piled high with local produce, with here and there a smallholder or gardener selling whatever vegetables he or she has harvested that day.

The island is lush. Its summers are dry but quite temperate, rain-washed from October, when the horta season begins. 'Horta' is a generic name for numerous varieties of greens, grown or foraged, which might include wild mustard, dandelion, curly endive, dwarf chicory, burdock, beet leaves, the bitter weeds lapsana and psalithaki, sweetish maiden-hair, spinach and escarole. In May there will be Neopolitan garlic in flower, and grape hyacinths. The mixed greens are fried with fresh bulb garlic and rigani (the flower-head of oregano), to make horta tsigar. They are used for hortopitta - baked in a pie.

Talking of 'baked in a pie', thankfully, the traditional rouvellopitta, robin pie, made with maybe 50 robins, is a thing of the past, but you can expect, in the countryside, in the hunting season, to see or at least hear the hunters taking a pop at the songbirds. It is against the law to shoot game within 200 metres of a village, but that did not prevent one guy from firing bullets at some hapless thrush, right beside us in a lay-by, where we had stopped to marvel at the mountain view.

'Unsentimental' would best describe the Corfiot attitude to the animals that live by and among them. Don't come here if you don't care at all for cats, which are draped over sills and doorsteps in every village, survive on scraps, and may insist on sharing your accommodation. Don't come here, either, if you care for cats too much: you'll end up staying and running a refuge.

Three well-fed, self-possessed tabbies were attached with single-mindedness to the Villa Alexina, where we stayed, in Perithia, five minutes' drive from Pythos. This is a typical stone house, modernised with taste and restraint, using traditional materials, with orange trees around the pool, and with every window framing a perfect view of sea or mountainside. Ben and Claudia don't own but rather organise accommodation, in villas, mountain cottages and apartments.

You will need a hire car to explore the 'delectable landscape' described by Lawrence Durrell in Prospero's Cell, which, a century before him, drew the ornithologist, watercolourist and humorist Edward Lear back time and again to Corfu. 'The more I see of this place,' wrote Lear, 'so the more I feel that no other spot on earth can be fuller of beauty, and of variety of beauty.' (Was it this that inspired him to write so movingly of the elderly man who never knew what he should do, 'So he rushed up and down,/Till the sun made him brown,/That bewildered old man of Corfu'?)

Now, for souvenir-seekers, two things not to buy. First, the local, day-glow orange kumquat liqueur - unless for someone you heartily dislike, in which case favour the bottle in the shape of Corfu. Second, regettably, local olive oil. There have been olives on Corfu since the Bronze Age, but it was the Venetians who encouraged the mass planting and cultivation of olive trees. It took them 200 years, from their arrival in 1386, it took a payment of 36 drachmas for every tree planted, but they created a thriving industry.

Today, the island would be unimaginable without the three million and more olive trees that cover a third of its surface. Gnarled, twisted, sculptural, incredibly tenacious, some centuries old, they are deep-rooted in history, being of an ancient and unadulterated stock called lianolia, producing small, slim, pointy black berries, according to James Chatto and Wendy Martin in A Kitchen in Corfu (New Amsterdam Books). 'The entire Mediterranean seems to rise out of the sour, pungent taste of black olives between the teeth,' wrote Lawrence Durrell. 'A taste older than meat or wine, a taste as old as cold water. Only the sea itself seems as ancient a part of the region as the olive and its oil.'

Now, 21st-century chemical farming has got in amongst all that. The pity of it is that, as Ben warned, many of the olives have been sprayed with organophosphates, posing a possible health risk. 'At last public opinion may force a more eco-friendly method to be adopted,' editorialised The Corfiot magazine. But, 'Even if it is, belatedly, it will take a long time for the environmental damage to repair itself, if ever.'

Still, Corfu's luxurious olive groves, with their silver leaf canopies, are very, very easy on the eye. So, too, are those parts of the coast that have not succumbed to package holiday sprawl. Walking on the beach late one afternoon, we had just one companion, a white and black dog, who broke off from his task of policing the seagulls, to greet us. It was mesmerising to watch the sea turn from azure to dazzling turquoise to palest pastel blue and pink with the dwindling light, as the mountains of Albania, across Apraou Bay, declared themselves boldly then faded away like a dream.

'I went to the beach with Molly yesterday,' Claudia told me in November as I sat in London, freezing, 'and walked for an hour, in a T-shirt, and it was just really, really lovely. It rains a bit for three months, and when it rains it can really rain. When the wind comes from the North it can be real bitter, and the mountains of Albania are covered in snow. But when the wind comes from the South, it's about 18 degrees; literally, one day can be one and one day the other.'

For Claudia, one of the great pleasures of the Corfu Kitchen is the social interaction. 'I like meeting people. I like to talk, I like the idea of bringing strangers together who have something in common.' She likes to mix and match the guests, in other words. If, however, a party of six friends or work colleagues should want to come, that would be great, too. They can even tailor their own agenda: the structure is not set in stone.

Be aware, however, that while the cookery days are not hard work, exactly, they are involving. They demand concentration. Joking apart - and there is a lot of joking - there is a serious intent to teach, which should be matched by the intent to learn. If that isn't for you, or you want a break from the stove, you can always simply rent a villa, then pick up the phone and summon the Invisible Kitchen.