Don't tell me the kebab's gone all posh? Not exactly ? but, thanks to Shish, its greasy, post-pub image has been upgraded

There's a kebab shop opposite the Willesden Green and Cricklewood Conservative Club's drab villa. Next to it is another, of sorts; a bigger, bolder, newer, glass-fronted challenge to the members' outlook. This is Shish, the first of what are supposed to be several such snazzy, open-plan places specialising in kebabs, a type of food that has an undeserved reputation as being only fit for drunks and sleazeballs. To improve their image, the schtick here is shish, or shashlik or sis or seekh – the ones on skewers grilled over coals, as distinct from the endlessly rotating doner.

Shish claims to take as its theme the food eaten along the silk route from Rome to China, passing through evocative places like Trebizond in Turkey, Samarkand, and Kashgar on the way. There are mezze dishes to start with, a dozen different shish to follow and a few desserts. With several notable Indian restaurants and a sushi one, Willesden is not a complete food desert. But Shish is clearly answering a call for somewhere funky, ethnic and inexpensive. On a Saturday night the clientele was exuberantly multicultural.

If it seems too bright and noisy, it owes that as much to Lebanese juice bars and the volume at which keening music is played on Middle Eastern buses, as to Western fast-food establishments. Smoking's banned, as you perch opposite the chefs around the serpentine counter. You can't book the stools, nor the only two tables for four, so groups might end up eating in a row. But there's a loungey first-floor bar for meeting, eating mezze, drinking cocktails (£6 each), smoking, and shouting over maddeningly loud music.

Two of my party live in Dalston, aromatic epicentre of ocakbasi, the Turkish barbecue cafés where skewers of meat are grilled over painstakingly nurtured troughs of charcoal. Salads are chopped to a Rizla-paper fineness and come seasoned with sumac, the tart-tasting powdered red berry. The bread is fabulous. This is the standard to which Shish should be aspiring.

Although mezze are meant for sharing, neither the seating arrangement, nor the miniature bowls they come in make that inevitable here. It doesn't help that you get three lamb samsa (crescent-shaped, pale-skinned dumplings from central Asia, filled with lamb) and three falafel, to make distribution between two difficult. The falafel, with a salty, minty yogurt dip, were as crunchy as they should be on the outside, two cigar-shaped borek of spinach, feta and walnut in crisp filo left us wanting more, and the taboulleh wasn't bad, though it was a bit greasy and didn't have that just-chopped parsley-and-mint freshness.

"I could eat these all night,' said one of our four. We'd vetoed duck and spring onion rolls, chicken in pandana leaves, and cucumber wasabi as likely to clash with the other choices, as mushy aubergine with lime and peanuts duly did. Shish come either in flat bread with salad as a wrap, or with one of three starches: rice, couscous or, if you must, chips. There are two vegetarian varieties, two sticks of fish, and the rest are lamb or chicken, straying as far from the route as Indonesia for a coconut, lemongrass and coriander flavoured satay.

Only a glass screen – technically known as a sneeze guard, I believe – separated us from the chef. We were close enough to feel some of the heat and the unease of sitting and watching someone working hard, and at risk of burning their hands on skewers that are shorter than those the real craftsmen use. The most experienced cook among us wanted to vault over the screen and take control of the cooking. "I like to see a relaxed-looking chef, he seems to be struggling," he said. Other than one man's urge to hijack another's barbecue, I couldn't see what the problem was.

When the kebabs arrived they were perfectly cooked and unusually good, except the fish. They're the most expensive – £8.95 for the swordfish, £7.95 for three fish shish, one of which was nasty, fatty salmon – and they're horrid. Perfect lamb kofte redolent of cumin; garlicky "Mediterranean" chicken shish, and the sweet and sticky Persian chicken marinaded in orange, turmeric and saffron all confirmed that their swordsmen can take on the best skewer tenders. The finely chopped salad, though it's only of garnish proportions unless you order one separately, is authentically sprinkled with sumac. Couscous was so-so, but the basmati rice, cooked with cardamom in an electric device, is delicious. Several types of bread (£1.50 for a basket), including crisp, flat discs sprinkled with dried herbs, come from a cavernous oven. Specialised equipment runs to a machine for squeezing whole oranges.

At the pudding stage, Shish also parts company with other kebab joints. There are sorbets, a top notch vanilla ice cream, and a lovely almond, plum and pistachio pastry – not as sweet and sticky as baklava. If the halva ice cream which accompanied it is a Shish invention, it may be one of the greatest breakthroughs in the history of cold desserts. Espresso comes in hip little cups. Even necking a lot of rosé, we spent only just over £20 a head.

What Wagamama did for noodle soup, Shish could do for skewers of meat; though I'd recommend it keeps to the promised path through central Asia and rethinks the fish sticks. As we left, post-pubbers were turning up at Willesden Kebabs and Burgers next door. Kebabs have had a bad name, partly for the company they keep; Shish should give them a good one.

Shish, 2-6 Station Parade, Willesden Green, London NW2 (020-8208 9290) Mon-Fri breakfast 7am-12, main menu 12-12, Sun 8am-11pm. Major cards, except Amex and Diners Club, accepted. Wheelchair access