The Straight and Narrow, 45 Narrow Street, London E14 (020 3745 8345). Meal for two, including drinks and service: £70- £100

It is anthem night at the Straight and Narrow in Limehouse, and the piano player is working his way through Dancing Queen, Wuthering Heights and Bonnie Tyler’s Total Eclipse of The Heart. He has a boisterous left hand, does Vaughn George Eunson. It pushes the melody on, imploring you to join in. Before I know it, I’m howling the chorus over the meatballs. “Young and sweet… Only severnteeeeen…” And so on.

I can’t pretend. I am predisposed to like anywhere furnished with a piano. Partly it’s fellow feeling. As a piano player, I am lucky enough never to have had to earn a crust playing to a disinterested restaurant; to the muffled chatter of the mating game, while rolling from one tune to the next. That’s proper work. It demands my support.

But it’s also the fact that any space occupied by piano has greater potential. Things can happen there. It’s relatively quiet tonight at the Straight and Narrow, but later in the week, they tell me, it will turn into a total singalong. If you hate the thought of that you are dead inside; go somewhere else. Try a graveyard, where the company will be more agreeable. Food and music are meant to go together. Jazz, which is what I have spent most of my adult life at the keyboard wrestling with, was born in restaurants like this – first in the drinking dens of New Orleans, then in the speakeasies and dance clubs of New York and Chicago.

I like to joke during my own gigs that the musicians in my quartet have watched people eat in some of the best restaurants in London. You can hear me making that joke in the live album we’re about to release. Partly it’s a collection of songs around food and drink, like Black Coffee, One for my Baby and Cantaloupe Island, tunes which celebrate the relationship between jazz and dinner. Others draw on my experience of growing up with a mother who was an agony aunt, because all blues songs sound like a problem page letter. Listen carefully to the recording and you can hear the occasional clink of a glass in the background. Music like this demands liquor and the sound of it. (If I said it was available for purchase from Amazon and also for download would that be overkill? Probably.)

In his memoirs Stephen Fry wrote about meeting the head of the Nederlander theatre dynasty in New York, who was thinking about bringing the musical Me and My Girl to Broadway, for which Fry had rewritten the book. For a musical to succeed, Nederlander said, it had to “have heart”. The same should be said about restaurants. The Straight and Narrow has heart. It does not occupy a pretty space. One side of Narrow Street is made of classic ancient warehouses, doubtless with interiors that glossy magazine editors would die for. The restaurant is on the other side, on the raised ground floor of a much more modern development. It’s not quite Peter Kay’s flat-roof pub, but it’s on nodding terms. What matters is that, inside they are both playing and cooking up a storm. Not in an ostentatious way, but with care and attention to detail. The Straight and Narrow is the neighbourhood restaurant you want around the corner; the one which will leave you feeling someone gave a damn about you having a good time without trying to extract a down payment on the Greek debt.

After my rant about Yorkshire tapas a few weeks ago I suppose I can’t really let them off the hook for having a section of the menu called British tapas. Except that those Yorkshire tapas were crimes against good taste and these are very lovely. We order three as a starter. A Scotch egg, with a golden shell made of properly seasoned sausage meat mixed with cubes of apple, comes with a yolk just on the edge of running. There is a finely whipped mackerel pâté, full of oils and acidity, with gossamer ribbons of pickled cucumber and melba toast. Veal meatballs, in a sauce of fresh tomatoes cooked down to the essence of themselves, are peppery and satisfying. All of these are priced at between £4.50 and £6.50.

Main courses, priced in the teens, offer the kind of European-inspired, bistro cooking utilising British ingredients that is the food we really want to eat most of the time. It is roast chicken with risotto and fillet steak with chips. The nearest thing to ostentation is soy-glazed pork belly with Asian slaw and salted peanuts. I only don’t order it because people have been gossiping about me and pork belly. They’re saying we’re a thing. I don’t like to encourage gossip.

Instead I have slices of a substantial piece of lamb rump, roasted to crisp fat outside, cherry pink inside, piled on roasted courgettes. At the base, soaking up the jus, is a disc of puff pastry laid with roasted tomatoes. A dribble of basil oil finishes it off. A slab of hake with crisped skin and pearly flesh lies on a meadow of summer peas and baby leeks dressed with a garlic butter sauce, with enough acidity to push it towards a beurre blanc. Dill gnocchi give ballast.

Desserts are exceptionally good, the sort that make you wonder if there has been some grand hotel training involved (although apparently there hasn’t). A salted caramel tart has dark pastry with an echoing crunch and a deep golden filling that stays the right side of cloying. A marmalade ice cream lives up to its billing without dominating the proceedings. A peach melba bavarois, alternate layers of mousse and sponge, with a raspberry sorbet on the side, demands a round of applause before you demolish the lot. Oh, but it’s pretty.

Service is engaged without being stalkerish. The wine list is short and sensible. In this room, you don’t want to think too hard about ordering the second bottle and these bog-standard sauvignons and pinot grigios are designed for that.

As the evening closes, somebody requests Billy Joel’s Piano Man which is a cliché but only so for being true. The musician in a restaurant creates the soundtrack for the inner lives of others. I am not quite a part of the regular crowd that shuffles in, but having eaten the food and drunk the wine and listened to the tunes, I could quite easily imagine becoming so.

Jay’s news bites

■ In New York, chef Marcus Samuelsson’s Red Rooster is part restaurant, part gig. The live music in the Harlem dining room is part of the draw. The same applies to the outpost in the Curtain Hotel, east London. There’s a changing roster of acts – including a gospel choir over Sunday brunch. It’s the perfect accompaniment to their Bird Royale Feast, a whole southern fried chicken with waffles, mac and greens and pickles (thecurtain.com).

■ It’s official. We really do want plates. A survey of more than 2,000 people by YouGov Omnibus found that 99% of people considered round plates acceptable. The least approved serving items were a shovel (17%), a dog bowl (10%) and a shoe (9%). You didn’t know some restaurants serve food in shoes? I envy you.

■ A respectful nod to the expanding craft beer chain BrewDog, which has announced it will give away 20% of its profits – 10% to charity and 10% to staff. The company says this could be as much as £45m over the next five years.

Email Jay at jay.rayner@observer.co.uk or follow him on Twitter @jayrayner1