Babaji, restaurant review: Hakkasan's Alan Yau has turned his attention to the Turkish pizzeria

53 Shaftesbury Avenue, London W1 (020-7327 3888)

Traditional with a twist: The casual vibe and higgle-piggle chaos of the service tells you it's a café, but the high-finish Ottoman/Oriental design makes a claim for something more fancy

It's shortly after noon, on a brutally cold Sunday. We're scoping out a new restaurant in central London which has opened quietly, without the usual PR fluff. It's got an odd, uncategorisable name. Babaji? What's that – Indian? No clues outside, though it looks smarter than the humdrum tourist traps which throng this stretch of Theatreland.

So how come every table is filled, and there's a queue forming as we nab the last four-top? What can have given this place its pull? The answer is Alan Yau. Chances are you've eaten in – or at least heard of – one of the restaurant brands he's created, which include Wagamama, Busaba Eathai and Hakkasan. Yau launches restaurants like Calvin Harris releases records, producing hit after hit, though his most recent offering, Naamyaa Café, failed to chart and was quietly deleted from the catalogue.

Yau announced his retirement from the restaurant game not so long ago, having sold his stake in most of his creations. Then he promptly started work on three new openings, with Babaji the first to emerge. Our fellow early adopters are queuing up to find out what Mr Y will reinvent this time, having democratised the noodle bar and Bangkok café, glammed-up the Chinese restaurant and imported the slick Milanese bakery. And the answer is – obviously – the Turkish pizzeria, or pide salonu. Just when we thought we'd reached Peak Pizza, the clever chap has come up with a new way of making bread with toppings seem all exciting again.

Pide – as Turkish-style pizza is called – is the Big Idea at Babaji. Long, puffy paddles of airy flatbread, topped with minced lamb, beef pastrami, corned beef and egg, feta and mixed herbs. Traditional with a twist, in classic Yau fashion. It's like they finally built the last stretch of motorway between Naples and Istanbul.

An enormous pizza oven looms over the cramped dining room, fed by sweating chefs who seem to be playing Twister round a beached space shuttle. Harem-panted waiters squeeze past diners squished on to benches. The casual vibe and higgle-piggle chaos of the service tells you it's a café, but the high-finish Ottoman/Oriental design makes a claim for something more fancy. The food doesn't quite settle the argument; it's possible to have two very different experiences from the vast and somewhat random menu which in places seems as authentically Turkish as the steakhouse that used to occupy this site was 'Scotch'.

There's finesse in a bowl of crisp, chilli-dressed fried squid, with its garlic-rich yogurt and walnut sauce. A heap of vivid baby samphire is served Turkish-style, simply dressed with lemon, garlic and olive. Beef and lamb kofte deliver a blast of transporting flavour; nubbly, charred patties oozing authentic garlic and smoke. And we swoon for the Topkapi chicken, roasted boned-out thigh stuffed with a cinnamon-scented, pine nut-studded pilaf. The house-made baklava, holding a loose honeyed rubble of pistachio, is wonderful.

It's the more traditional dishes, though, that fall slightly short. Paste-like, underseasoned hummus; tepid, pliable cheese and spinach-filled borek; chickpea and lamb stew which is a bit too close to home cooking for comfort.

And then there's the pide. Served at the end of the meal, after the main dishes, they should be the highlight, but they're oddly forgettable. The bread is great, crisp and pliable, like the lightest pizza base. But the minced lamb topping doesn't register, and a spinach, red pepper, baked egg and feta variety comes over like the unpopular veggie option at Pizza Express. There's something missing, too, in the presentation; we watch them emerge from the oven, foot-long and spectacular, but by the time they've been sliced and piled on a platter with pointless heaps of salad, they've lost their razzle-dazzle – unforgivable here in the heart of Theatreland.

I leave Babaji not quite sure if it works. The chaotic service (dishes arriving out of sequence, staff who struggle with simple questions), the plangent violin music which could soundtrack a movie about a Turkish farmer forced to eat his last sheep. It's all a bit discombobulating. But returning for supper a few nights later, I like it better; service is smoother and smilier, the atmosphere is warmer and the food is more consistent.

And the rest, as they say, is geography. There are great places to eat all around Shaftesbury Ave, but not too many slap bang on it, where you can dine well for £15 a head. Babaji, in short, is handy, and the no-bookings policy makes it a good option for a pre- or post-theatre bite. I wouldn't presume to offer advice to an operator as seasoned as Alan Yau. But he may need to tighten up the menu and focus on making those pides shine before Babaji takes its place in his greatest hits collection.

Food ***
Ambience ***
Service ***

53 Shaftesbury Avenue, London W1 (020-7327 3888). Around £15-20 a head before wine