101 Upper Ground, London SE1 (020 7452 3630). Meal for two: £60

The Green Room, across the road from the back of the National Theatre, is a great opportunity currently being squandered. It is, by any measure, an intriguing venture. The National Theatre is rare among major arts institutions in being located amid a residential community; one nurtured by the Coin Street Community Builders, a social enterprise body which, since 1984, has been instrumental in developing the slab of land on the Thames’s south bank which houses the theatre. It means the National has neighbours. Now, in partnership with the Coin Street Community Builders, the theatre has opened a neighbourhood restaurant. Or attempted to. I’m just not convinced, given what else is available, that the neighbours will be overjoyed to have it in its present state.

But let’s first look at the good stuff. It’s housed in a beautiful, glass-walled shed, designed by the recently graduated architect Benjamin Marks. There are pillars made from repurposed granite London paving stones, and raw wood beams. There is a bit of industrial ducting, a certain amount of exposed chipboard and an awful lot of space and light. The glass walls look out on to lawns and gravelled terraces which, doubtless, come the summer, will be populated by tables and chairs. Even on a short, grey January day, with the available daylight quick to fade, there is a sense of freedom.

The involvement of the National is pointed up mostly by a set of glass-topped cabinet tables, enclosing props from productions of War Horse, A Small Family Business and One Man, Two Guvnors. For anybody who’s seen, say, War Horse, it is genuinely intriguing to witness the care that has gone into props – documents, paper-wrapped packages of tea, carrots for the horses – the details of which will pass the vast majority of the audience by. Less successfully they have attempted to re-use unsold National Theatre programmes by sticking the beer and wine lists into them. Just a few weeks into the life of the restaurant and the glue had already given up the fight so that, when picked up, pages fluttered out like so many sales leaflets from a Sunday newspaper supplement.

Still, their heart is in the right place. They are at pains to tell you that the handles of their cutlery are moulded by a not-for-profit community training group in South Yorkshire. Their crockery comes from a company with the lowest carbon emissions of any hospitality tableware firm anywhere in the world. The stationery is made from 100% recycled paper. The tables are made from wood from carefully protected forests, and they made sure no river nymphs were harmed in the restaurant’s creation. I may have made the last one up. You get the idea. You’re meant to feel brilliant about yourself before you’ve eaten anything.

Sadly, I’m not sure there’s quite enough of this stuff to compensate for the dead hand on the menu. Yes, the kitchen can cook. There is a short list of things to pick at, which we rather like. Crisp, deep-fried salt-cod croquettes come with a good coarse-cut sauce tartar. Potato skins filled with cheese, almonds and a kick of horseradish are dispatched quickly. The portion of hot Lincolnshire poacher rarebit with crispy pancetta may be on the miserly side for £4.50 – three slices through a thin baguette – but it’s well made. There are well-dressed side salads and the chips are very good indeed, which is so rarely the way. They make the right tissue-paper rustling noise, and come with their own pokey ketchup.

The problem is the rest of the menu. It’s built around a burger, baby back ribs, a flat-iron steak and a “hot dog”, which will have to remain deep inside those quotes until I get to it. London has loads of places doing these things very well indeed. You can’t move for bespoke burgers dribbling sauce down your wrist, and they’ll cost rather less than the £9.75 charged here, no fries included.

It doesn’t matter that it is “Prime Buccleuch beef” if the result is merely adequate. It does matter that it’s Monterey Jack cheese, which even at its best is a gasp of nothingness compared to the salty-sour cheddars widely available here. They do not ask how we would like it cooked. You can have it any way you wish as long as it’s medium, medium or medium. They may claim environmental health officials barring pinkness. If so, I would choose to go somewhere else that has found a way round the problem.

Sticky baby back ribs are merely fine, but less so given the portion size for £10, again compared to what’s available elsewhere. The hot dog is nothing of the sort. It’s a spiced pork sausage, and an overly spiced one at that. This is clearly an item children will gravitate towards. Giving it a kick like an angry mule is not smart. Cue lots of dish swapping on our table so the child gets something they can cope with.

None of these things is terrible. Underwhelming, yes. Baffling, certainly. But not terrible. By contrast the flat-iron steak is dreadful. They confirm it has, as suspected, been water-bathed first. This has benefits for the kitchen. They can just take it out of the bag, sear it on the grill and the job is done. For the diner the result is something floppy and raw-tasting, marbled with ribbons of connective tissue. Yum? Not so much.

It’s all terribly unimaginative, and a letdown compared to the ambition of the building which houses it. The whole thing feels like it has been designed by consultants, who have spent too long looking at the restaurant options available on the river side of the National Theatre, and attempted to fill gaps which aren’t worth filling. Artistically, the National has always made a point of being popular without aping what’s available in the commercial sector. Its restaurant should surely do something similar.

Happily, everything perks up at dessert, to such a degree that I wonder out loud whether they are made on site. I am reassured by one of the eager and efficient waiters that they all are. There is a very good burnt Alaska, a killer sundae, passable profiteroles and an excellent multilayered sponge cake, made with honey from hives located on top of the theatre, which is a nice touch. The problem is that any number of nice touches like this, and the Green Room has loads of them, can’t compensate for a main menu that’s a dull thud.

Jay’s news bites

■ For another restaurant which engages fully with the local community, try Waterhouse on Regent’s Canal in Shoreditch. Owned by the Shoreditch Trust, which works to reduce social and economic disadvantage locally, it pays attention to the food. Go for butternut squash risotto with chestnut mushrooms, confit duck with chive mash and Granny Smith crumble (waterhouserestaurant.co.uk).

■ Anybody with both a taste for wood smoke and deep pockets will want to know that the company behind the Bertha wood-burning oven used at John Doe Restaurant, reviewed here two weeks ago, will have a model for the consumer market by June. Yours for £2,500, which is less than half the price of the restaurant version (berthaoven.com).

■ Time to celebrate an outbreak of good taste. Before Christmas, Amazon was flogging Breaking Bad Crystal Minth Candy – a small baggie of mint-flavoured sweets made to look like crystal meth. How witty! A few days ago it was withdrawn from sale. Hurrah.

Email Jay at jay.rayner@observer.co.uk. Follow Jay on Twitter @jayrayner1