As glam rockers Mudd might have chanted, looking left and then right at the second floor of the Oxo Tower: "That's Neat, that's Neat, I really love your dining feat." It is no small feat, this new restaurant, for Neat is a place of two halves on one enormous floor of the landmark riverside building. One half is a brasserie, the other's devoted to a higher level of gastronomic achievement. It should be a major step forward in eating out in London, although in its first week it was occupied sparsely and almost exclusively, when I first went, by reviewers.

First, I turned left for lunch, to find the brasserie decorated in a style that's peculiarly French. Mauve leatherette banquettes and chairs against coppery orange walls compete with a river view that on a dull day reminds you how brown the Thames can look. Then there was the music: terrible cha-cha-cha Europop. Not everything French exports well (mind you, Mudd weren't anything to write home about, either). But in such gifted, albeit English hands, the cooking easily asserts its superiority over many London restaurants. Richard Neat has travelled. From Pied à Terre in Charlotte Street where he earned two Michelin stars, via an Indian hotel group, to the south of France. There, his restaurant, unusually for an Englishman abroad, has a Michelin star. He is not, according to accounts from women journalists, an easy interviewee; as a chef he's capable of charming his customers, and the London restaurants can accommodate scores of them, although he'll be spreading his efforts between here and Cannes.

Even the brasserie offers something way above the ordinary, and is priced accordingly. Starters begin at £7.50, mains at £13.50. Of a dozen fabulously original choices, of which we both resisted picking deep-fried oysters with rouille, we tried oxtail ravioli, a crepe-thin skin over shredded meat, with small, sweet, tender borlotti beans in lovely meaty juices. Given the amount of work, £8.95 didn't seem excessive for the second starter: a ballottine of quail. This included two juicy little legs, slices of gamey, herby quail-meat sausage, waxy potato sharpened with balsamic vinegar, mushroom duxelle, green beans and quail's eggs. A busy but not fussy dish.

Main courses were excellent, too. Haddock with clams and a saffron-gilded cream sauce had a couple more sheets of the show-off thin pasta underneath, and threads of leek and carrot, flavoured with what could have been white pepper, on top. Another fish dish was chosen on the grounds that most of the meat seemed too wintery; we didn't want lamb confit and parsnips or braised ox tongue with cabbage and turnips in June. However, the "tower of calamari", alternate clusters of tentacles and of the smooth body sliced into petals and stacked one upon the other, was stunningly good. The squid, tender but with surface crispness, was surrounded by a superb sauce gribiche, the classic mix of finely chopped hard-boiled egg, vinegar, capers, and tarragon, with lemony oil round the edge and wilted salad leaves. Finally, oddly, and without irony, there's a dessert trolley. A slice of pear and almond art was fruity, sticky, very sweet but no better than you'd get in a top patisserie. For £7.50 a bit more artistry, and some cream, might have been expected.

If this, at £77 for lunch of two and a half courses each, water, coffee, no wine, was the cheaper part of Neat, what, and at what price, could be expected on the other side? "I'd pay more to get away from the music and these colours," sniffed Bob. At lunchtime you don't have to pay much more, and indeed, turning right the following night, it was blissfully calm. The carpet helps, so do the plum leather bucket chairs and grey walls. Along the back wall the row of semi-circular banquettes are arranged so everyone faces the river, which is far more fetching at dusk than in daylight. "But why does it have to be so sombre?" wondered Dick. Because you're in the presence of seriously great cooking, with the attendant solemnity, punctilious staff and a lofty, in height though not manner, Danish sommelier. First we got to taste the oysters I hadn't had in the brasserie as the pre-starter freebie. With a saffrony rouille and tiny sticks of fried courgettes, it was a glorious beginning.

Starters: the strange but tempting-sounding red mullet rillette with prune purée and almond cream, and snails with morilles, garlic purée and asparagus. The soft cylinder of mullet topped with a layer of prune didn't taste remotely of the sea. "I'd have been pushed to identify it as fish," said my consort once I'd eaten the most telling clue ­ part of the pretty pink skin cleverly turned into a crisp shard. But the snails, each one coated in unidentified but magic mousse, dusted with mushroom powder, on more funghi and garlic, and with asparagus sliced lengthways, though very contrived was one of those memorable how-does-he-do-that improvements on nature.

Turbot, with more of the wafer-thin pasta as lasagne layered with the sweetest little shrimps, was lapped by mushroomy bouillon, a teasingly complex elixir that made me want to remove every molecule from the plate by whatever means necessary. Pigeon breast was the plumpest and tenderest ever, with little globes of white bean gnocchi, a pea velouté and around the edge, like an embroidered border, stitch-sized pieces of carrot. This was very fine cooking. The sweet freebie almost eclipsed the puds themselves. A miniature crème brûlée with wisps of citrus zest and lime sorbet on top was truly exquisite. Neither mango slices arranged around a bombe of creamed rice with more of the lime sorbet, nor an apricot tart tatin made an overly sweet ending, and the patisserie section showed more lightness of touch with the petits fours. Strange as it sounds, it was not an excessive meal, but delicate, subtle, wondrously successful. With lunch in the restaurant at £29, the cost differential between this and the brasserie makes it the more appealing choice ­ especially for the colour ­ as well as price-sensitive. Dinner is the restaurant is unlikely to cost less than £80, twice what it'll be in the brasserie. Either way it'll be Neat.

Neat brasserie, second floor, Oxo Tower Wharf, Bargehouse Street, London SE1 (020-7928 4433). Daily lunch 12-3pm, tea 3-6pm, dinner 6-11.30pm (Sun 10.30pm), Neat restaurant (020-7928 5533) Mon-Fri lunch 12-2pm, dinner 7-10pm, Sat dinner 7-10pm. Cards accepted, no Amex or Diners. Wheelchair access. Lunch £29, dinner £49