Tinello isn't a child of the Georgio Locatelli empire, more a friend of the family. The co-owners are brothers, Federico and Massimiliano Sali, who used to be, respectively, head chef and sommelier at Locanda Locatelli – the grand Italian restaurant where Bill Clinton and Madonna used to eat when in London. Locatelli has apparently supported the Sali brothers in their new venture – and there's a warm, knowing-what-we're-doing feel about the place when you walk in.

The first thing you notice is how dark it is in there. Little plate-sized circular lamps on adjustable wires cast cones of light over individual tables, as if the seated diners were about to play poker. One wall is exposed brickwork, something that always works in restaurants, while the facing wall is laid with black shiny tiles, as if we're in a modern bath showroom. The whole restaurant is so dimly lit that some patrons hold their menus at arm's length to read them – but the bar at the end has a bright, stylish array of wine glasses on glass shelves.

The clientele represents most age groups, from the young couple in jeans (him) and white maternity smock (her) to the elderly pair who coolly ordered the £35 house special of pasta with shaved black truffle. Behind our table, a quartet of laddish Mediterraneans (three Spanish, one Italian) sat flooring red wine and joking into the afternoon, as if hanging out in a Palermo drinking club. It was, said one of my companions, rather sexy.

I couldn't say the same for the menu, which seems, at first sight, a little bland and predictable. There are two speeds of starter, Antipasti and Small Eats: from the former, only the calamari and, chickpeas, potatoes and chilli stew stood out, and it would be a brave man who starts lunch with a filling combination.

The Small Eats offers titchy plates of, say, prosciutto, deep-fried octopus and deep-fried baby artichokes. We tried some: the deep-fried baby cuttlefish was tasty enough, but the batter had the consistency of flaking plaster. Crostini of Tuscan chicken liver was much better: slices of toast with brown sludge has seldom tasted so appealing.

There's a common problem with fancy Italian restaurants: the pasta. If it's made in-house and cooked perfectly, silkenly but unyieldingly al dente, it's still, you know, only pasta. If they do fancy things to it, it'll lack authenticity. If they make it with a simple tomato-and-basil sauce, you ask how they justify charging £10 for it.

At Tinello, Angie's pappardelle with cep mushrooms was advertised as "the perfect winter lunch, with a lovely fungussy aroma, and a fine texture to the mushrooms". My Pastificio dei campi with Nduja and burrata looked messy: the pasta pieces were the size of the roll-necks on beatnik jumpers in the 1950s, the nduja (a kind of dense sausage spread) was incorporated into the slimy sauce, and the burrata (a milkier version of mozzarella) sat on top like cottage cheese. It was tasty and spicy, but nothing worth igniting a fiesta about.

The mains, however, were electrifying. It was as though Locatelli himself had strode through the kitchen, shouting, "Raise your game everyone! Let's see some excitement out there!".

Albert's char-grilled baby chicken, spatchcocked and cooked to a smoky turn, was a knockout; it lay on a bed of diced roast potatoes with spiced peppers and a side order of fried tendrils of courgettes, spilling from their container like the green hair of the Gorgon Medusa.

"D'you want to try a very small bit," asked Albert (aged 13), "before I finish it?" (I take this to be a big compliment to the chef.)

Angie's roast fillet of cod with celeriac and anchovy sauce drew cries of rapture. "It's rare to find a piece of cod so fresh and delicious you could eat it by itself," she said, "but the celeriac goes with it so beautifully, it's overwhelming." I happily joined in the chorus of praise.

My veal chop, slow-roasted for ages with bay leaves and juniper berries, was wondrous, a big butch steak on a bone the size of a handlebar. But the highlight of my dish was the fennel – a giant lump, sliced in half and slow-braised with the veal until it was sweet and melting. I thought I knew everything you could do with fennel. And I never thought slow-cooking huge chunks of it would pay off. But that's why you look to chefs like Federico Sali to enlighten you.

A classic tiramisu – moist, then creamy, then almondy and alcoholic – nearly finished us off; then a slice of almond tart, slightly dry but enlivened by lemon-yoghurt ice-cream, delivered the coup de grâce.

We left Tinello, stumbling out into the mid-afternoon traffic of Pimlico, after two hours, feeling we could have stayed there all day. The restaurant is a brilliant combination of family-hearth comfort food and intensely-flavoured gastro style – a lovely hybrid of Umbria and Chelsea – and I urge you to try it.

Tinello, 87 Pimlico Road, London SW1 (020-7730 3663)

Food 4 stars
Ambience 3 stars
Service 4 stars

About £80 for two, including wine

Tipping policy: "No service charge; all tips go to the staff"