You can't guarantee that art galleries and museums will boast wonderful eating facilities. In 1988, the Saatchi brothers wrote an ad campaign describing London's Victoria & Albert Museum as "an ace caff with quite a nice museum attached" but few people were impressed with either the slogan or the food. Maybe, after two hours of inspecting Last Suppers, still-life dead pheasants and fruit portraits by Arcimboldo, the last thing the art-lover wants is a hearty lunch. And in many galleries, you won't get one.

In the Royal Academy last week, checking out the summer exhibition, I found in the restaurant a choice between cold salt beef with potato salad or hot stew with rice. It felt like a glorified canteen, full of rumpled aesthetes reading the New York Review of Books. I suppose that, where there's a horde of spectators passing through your gallery all day, you shouldn't encourage them to linger. But what if some punters come there for a day out, hefty repast included? How do you balance the five-minute-snackers and the people looking for three full courses and the Chilean merlot?

One gallery that seems to have cracked this dilemma is Pallant House in deepest Chichester. The house is an ace Grade-1-listed, 1712 Queen Anne townhouse with quite a stark modern wing attached. Currently the gallery is exhibiting the beautifully, crazily surreal visions of Leonora Carrington and her best friends, the equally unhinged Remedios Varo and the comparatively down-to-earth Hungarian photographer Kati Horna.

Carrington often portrayed the trio as witches or as a spooky sisterhood, preparing and cooking food inside a magic circle. There's clearly some magic going on in the restaurant as well. The kitchen is ruled by Sam Mahoney, who learned cooking under the Roux brothers and was head chef at Kensington Place, before leaving two years ago to start his first Field and Fork café-restaurant in a quiet square in Chichester. The Gallery version seems, at first glance, so small that you worry claustrophobia may overwhelm you; but then you see the other tables outside the glass wall under a canopy of slender trees, overlooked by industrial sculptures like Victorian pasta-making machines. The decor is a neutral cream-grey, contrasting with a collection of 18th-century china figurines, teapots, vases and the like, redolent of the old house, that are displayed behind glass, in red caves in the back wall.

Lunchers on different time-schedules can choose from soup, sandwiches, salads, eggs, light lunches and mains and (for £22.95) enjoy possibly the only Sunday set lunch in the country that doesn't involve beef and Yorkshire pudding. My date's starter of smoked eel, three substantial tranches on a bed of shredded carrot and sesame, was tender, moist and yummy, the eely wedges like kippers plumped up with ambrosia and tickled with a dressing of sweet soy and ginger. My tagine of quail was cooked to a perfect tightness of texture, accessorised by heftily flavoured artichokes and broad beans – and I appreciated a cold and crispy garnish of cucumber. A trickle of delicious jus turned out to be a concoction of cumin, cinnamon, star anise, ginger, black onion seed and quail-bone stock, and I greedily wished there'd been more of it.

Main courses were equally rich and substantial. My friend's jambonette of black leg chicken was a hugely elaborate structure, about the size of Tracy Island in Thunderbirds: an island of vegetables constructed like a butch risotto of peas, spinach, broad beans, asparagus, artichoke leaf and finely sliced truffle, sitting in a sea of watercress soup. The chicken had been de-boned then stuffed with chicken and truffle mousse and served in toothsome slices. "Frankly," said my date, "I'd be satisfied eating just this plate of vegetables – but the chicken is really delicious."

My slow-roasted pork belly, glazed with sweet soy sauce, was dark, intense, mysterious and delicious. The layer of fat in a pork belly can be a tad squelchy, but it here was full of succulent unctuosity. Around it, as though in a stalled procession, came carved courgettes, sculpted potatoes, trimmed carrots and soft asparagus, all thoroughly cooked without coming anywhere near mushy. Two tall thin sticks of crackling stuck out of the dish like antennae, and were utterly fab.

Punters were still arriving at 2.30pm, to be greeted by our indefatigably charming waitress, Janine, as if they were old friends. Our puddings were presented like two more mini-islands. Roast white peach with strawberry mousse and almond caramel sauce was as yummy as it sounds, sweet and warm with a welcome crunch of almonds. I couldn't taste the herb in my lime and basil pannacotta, but its texture was faultless, and the champagne-poached strawberries would have made an angel weep.

To find such superior, perfectly judged, confidently flavoured cooking anywhere on the south coast is a revelation; that it should be found in an art gallery is frankly astonishing. Leonora Carrington and her cauldron-circling sisterhood would have been so proud.

Field and Fork, Pallant House Gallery, 90 North Pallant, Chichester, West Sussex (01243 770827)

Food 4 stars
Ambience 3 stars
Service 4 stars

About £80 for two, with wine

Tipping policy: "Service charge is discretionary, and all tips go to the staff"