Frankie's Italian Bar and Grill, 3 Yeoman's Row, London SW3 (020 7590 9999). Meal for two, including wine and service, £65

It takes rare talent for a restaurant to snatch defeat from the jaws of victory. It takes even more to turn it around and snatch victory back from those snarling jaws of defeat. Frankie's Italian Bar and Grill, in London's Knightsbridge, managed just that. Put aside the hilarious Z-list celebrity naffness of the joint being named after championship jockey Frankie Dettori, a man whose entire career depended upon him being able to survive on a diet of rice crackers and grass clippings, and who should probably therefore have nothing to do with restaurants. The truth is that this is not a Dettori venture. It's a Marco Pierre White venture, badged with Frankie's name.

I will confess that I have not been overly impressed by Pierre White's restaurants. Too much form. Not enough content. For a while he has seemed to be hunting around for a restaurant concept he can build into a chain. Prior to this basement site becoming Frankie's, he ran it as a Chophouse Parisienne, a serviceable but unsuccessful brasserie, and then, ditto, as Chez Max. It was all red walls and oversized Gauloise posters.

Now it's giant sexy mirrorballs, mirrored walls, brown-paper tablecloths over folds of red leather, and pizzas. It's a funky, buzzy spot of the sort the Americans do well and we don't. I went with my family for Sunday lunch when, pleasingly, it was overrun with kids, and it was a joy to behold. The menu works because it doesn't overstretch itself. There's a short list of starters - calamari, Parma ham - for around £6. There are five pastas, 10 pizzas and a bunch of grills all hovering between £10 and £13, and an Italian wine list with loads under £20. The pizza bases are crisp, and serious care has gone into the choice of toppings. The salami is the real deal, and though a little overspiced for my five-year-old, a satisfyingly meaty mouthful all the same. There was a generous serving of porcini on my mushroom pizza. We liked the light but flavourful tomato and basil soup, and the outrageously thin-cut deep-fried courgettes which my one-year-old attacked like a hoover switched to turbo.

We might also have liked the hamburger my wife ordered but it didn't turn up. Ten minutes after the rest of our food had arrived, the waiter admitted they'd run out of buns and gone out to buy some more. This is a failure on so many levels: of buying by the kitchen, and of communication between kitchen and waiters, and between waiters and punters. There is nothing worse than a family forced into unsynchronised dining. Oh dear. Frankie's had been doing so very well.

But they turned it around. They comped her a plate of the special, the roast beef with Yorkshire pudding, and it was very good, tender meat and very good, crisp Yorkshire plus a perfect horseradish sauce. They also comped the puddings, a Pavlova for my five-year-old, with the crunchiest, chewiest of meringues, all of which he declared the best pudding he'd ever had, plus a terrific chocolate mousse for me. (And don't assume they did this because they knew who I was; if they had, they wouldn't have screwed up in the first place, would they.) They served terrific coffee, and at the end of lunch a magician came to our table and made our children gasp by doing things with scarves and ropes, and then made all of us gasp by getting a 10p piece inside a San Pellegrino bottle. It was, quite simply, a lunch rich in magic, and of so many kinds. We'll be back.

· Jay Rayner's novel, The Apologist, is now out in paperback.