Sir Terence Conran likes his cigars. That’s why his big project in Shoreditch has, in addition to the main restaurant underground and an excellent street-level cafe, Albion, this open-air bar and grill on the top. It’s for trophy puffing from on high.

As a sign of intent, there’s even a grotesque humidor on display, in the shape of an elephant — bought by Sir Terence at a charity auction in Cuba “after he had consumed a considerable quantity of rum”, his own publicists say, to excuse the eruption of tastelessness.

The Rooftop professes to be open “year round from midday until late, seven days a week, weather permitting”. What that means is that it closes when it rains and doesn’t open if rain is even speculatively forecast, so, being off Shoreditch High Street rather than in sunny Provence, it’s often shut. There’s a Twitter feed to report on the current state of play (www.twitter.com/boundaryrooftop) but it’s only erratically updated.

The restaurant seats only 48, some tables being semi-communal, although there’s also a sitting area just to drink. The space circulates around a central bar and grill; teak decking and quite low glass walls around the sides keep the feeling open. Planting is by Nicola Lesbirel and, although two large potted olive trees in the centre don’t look too healthy, the metal troughs along the edges are charming, featuring feathery grasses and vivid perennial geraniums.

The view is fully 360 degrees of London skyline, yet not especially exciting. Although you can spot the Gherkin and the odd minaret, it’s mostly just office blocks and grubby roofs. It’s a funny little enclave, stuck up in the sky, cut off from the street, only a bit bigger than some private roof gardens.

The short menu, though, is well thought out and now seems proficiently delivered too, contrary to some early reports. Niblets “for the table” are generously proportioned. Mediterranean breads and oil (£2.50) were a great carby collection, one full of pesto and pine nuts, another packed with sundried tomato and whole softened cloves of garlic. Cervelle de canut (£4.50) is not, as it sounds, a serving of brains but a delectable and user-friendly Lyonnaise speciality: a creamy soft cheese dip, composed of chilled fromage blanc, whizzed up with finely chopped shallot, lots of green herbs including chives, and a dash of vinegar, served with little crisped roundels of bread for dipping.

From the grill, there’s a short list of mains — lobster, rib-eye steak (with a little marrow on the side), lamb cutlets and the like. What you get here is basically top-notch barbecue fare but served not on picnic plates but lovely heavy white china with stylish cutlery: all those reminders of Conran family values ...

A fillet of sea trout (£14) was perfectly cooked and served absolutely simply with a slice of lemon and a little watercress. Anything more would have spoiled this melting delicacy. A sane luxury. A spatchcocked poussin (£14) came robustly grilled, accompanied by a sauce vierge, made of chopped green herbs in oil and lemon, tangy and refreshing, if a bit over-minty for me. A side order of chips (£2.75) was great value, a huge bowl of big hand-cut pieces, too much for two, even though so crisp and tasty that it was hard to stop.

The brief choice of puddings was just as enticing. A petit pot au chocolat (£5), served warm, with crumbly shortbread fingers, was indeed tiny but so fabulously rich, so definitively chocolatey without being too sweet, that it was completely satisfying. Garriguette strawberries (£7) were served unhulled, so you could eat them with your fingers, dipping them into vanilla-flecked thick cream.

Cocktails are £8, bottled beers £3.50. Unlimited filtered water, still or sparkling, is served in jugs for a cover charge of £1. The brief wine list is tasteful — not a single rude New World red, thank you — albeit steeply priced, opening at £19 a bottle. Obviously what anybody in their right mind wants to drink with such a meal on a summer evening is a decent Mâcon — and, being nothing if not an elevated expression of Sir Terence’s Francophilia, Boundary Rooftop has the ideal bottle, a butterscotchy Mâcon-Vergisson “La Roche” from Verget. Alas, it’s a stinging £35, or £9 per 175ml glass, despite being rustically served in a tumbler.

You could have an enjoyable time here on a sunny day much more economically, just having a drink or two while making hay with the breads and that herby dip. It would be a pity to deny oneself though. Playing a walk-on role in Sir Terence’s dream world is such a treat. Worth paying up for. Even if you don’t fancy the cigar.