The Old House by Shoot the Bull, 5 Scale Lane, Hull HU1 1LA (01482 210 253). Meal for two, including drinks and service: £40-£100

Chris Harrison knows how to do a lot of things. At the Old House pub, Hull’s oldest domestic building, he seems determined to do most of them. Perhaps this is driven by necessity. Hull may be the City of Culture, a place of fine maritime history and Larkin’s rhythmic misanthropy, but it isn’t quite the city of food culture right now. Scan the horizon for good restaurants and inevitably you end up circling around the much-written-about 1884 Dock Kitchen. It’s the local restaurant of quiet ambition, the one everyone’s heard of, that place where they do the thing. Where, as it happens, Harrison was once head chef.

If there are very few places of note in a town, that’s because finding the customers is tough. Let’s not dodge the issue; being City of Culture is brilliant and will leave an encouraging legacy, but many people here are still preoccupied with issues a little more pressing than nuanced cookery. Hull is, for example, among the 20 local authorities with the highest rate of child poverty. And when you start quoting poverty statistics in a restaurant review, you know you are dancing on the razor’s edge. So note to self: for God’s sake don’t swing into town sneering about the lack of bijou bistros knocking out a passable pot au feu, and waving your velvet cuffs in frustration.

Here’s something worth knowing. One of Hull’s great culinary items, served in chippies across the city, is the pattie: mashed potato, mixed with sage, battered and deep fried. I tried one recently during a recording in the city of an episode of Radio 4’s The Kitchen Cabinet. Put a pattie in a bap and it becomes a very classy chip buttie indeed, all crunch and softness and breezy aromatics.

Once upon a time they were fish cakes, made from the catch landed at the docks. Eventually, however, as the local economy contracted, the catch left the city, destined for people who could afford to pay for fresh fish. So now the pattie is a fish cake without the fish. When social, economic and food history slam into each other like that, the challenge to a local chef of ambition becomes clear.

In those circumstances, you have to do what you can to attract as many customers as possible. Hence Harrison’s Fisher-Price Activity Centre of a menu: it can do this, and this, and that and the other. It will be whatever you want it to be. Harrison runs a major street food operation called Shoot the Bull. That continues, alongside this restaurant, inside a bricks-and-mortar pub. Half the menu reflects those street food origins: its fried chicken sandwiches, things on flat bread and variants on sausage and mash. There are mentions of mac and cheese. The other side draws on his experience elsewhere: as a cook at the Olive Branch in Clipsham, the Hand & Flowers and the Fat Duck. There’s a smoked pigeon salad, venison with ratatouille and a whole section, slightly weirdly, dedicated to expensive Wagyu dishes.

It reads like a hotel menu, and those are exceptionally hard to pull off. In truth, Harrison doesn’t quite manage it. But there are flashes of brilliance, and things that could be really good with a little work. For example, he serves a terrific sausage roll for £1.50, all flaky pastry, ripe pigginess and the sweet, dark tones of caramelised onion. Only he serves it stone cold and deathly. It’s a promise unrealised; a disappointment in a heavy pastry overcoat.

There’s a similar problem with two main dishes. Slow-cooked then seared lamb shoulder comes with a salsa verde of pungent wild garlic, alongside tomatoes and feta. So there’s salt and soft and huge wafts of funky, damp thicket. A fillet of beef is seared accurately and introduced to good companions. There’s confit potato, and broccoli roasted with sesame seeds and, hiding at the bottom, a small amount of butter with a little miso. Everything on these plates has been done right. It’s all perfectly accurate cooking. But where’s the bloody sauce? Both of them are bellowing for jus or gravy, for a glossy reduction of cow foot or chicken wing or both.

Then again, nothing will improve his slabs of long-braised then barbecued pork belly with a crisp fennel slaw, a crunchy salsa made with watermelon, a glug of sweet, sticky sauce, all laid across warm, fluffy flat bread. Yes, it’s street food. The bread is daring you to wrap it all up and stride manfully out the door. But it’s also rather civilised in here, in this low-ceilinged pub, with the guttering of candles, even on a summer’s lunchtime. It’s a fair old plateful for £8.

I am very much taken by their whitebait, soft-bellied and crisp backed, with a Bloody Mary mayonnaise and a sprinkling of something called vinegar powder to remind you that you are at the seaside. I don’t care what it actually is; there’s a fine acidic edge, which does the job.

And so I am loitering in that hellish place for someone trying to tell the restaurant’s story: a place which could be great but somehow isn’t quite making it, simply because of a lack of attention to detail. Then a side dish turns up. It’s garden peas with smoked bacon and confit silverskin onions, held together by a rich, buttery stock. It’s their take on petit pois à la française. And it’s brilliant, the simple piece of cooking which restores faith. It was the dish that made me nod slowly and mutter pompously to myself about potential.

Strip down the menu, pay attention to detail, focus on the things you’re really good at, and the Old House could be something special. As if to remind us that this really is the case, a baked cheesecake arrives, with salted caramel ice cream and a dollop of strawberry jam. The texture is right. The balance of sweet to salt is good. But while it tasted of peanut butter, as the menu had promised, nowhere was there any banana, which was also promised.

Will Harrison take all this on the chin? I’m not sure. He does a good line in self-promotion, giving equal billing on his website to restaurants like the Fat Duck where he merely did work experience, to those he was actually paid by. But there is ambition and talent. It’s just about getting the two things to come together at the same time.

Jay’s news bites

■ Pitt Cue started as a street-food operation on London’s South Bank. Back then they were trailblazers for American BBQ. In their most recent restaurant in the City, they have a grown-up English accent. Go for cured and smoked jowl, onglet with king oyster mushroom and ox tongue with celeriac (pittcue.co.uk).

■ For those going to Edinburgh the brilliantly funny George Egg is back with a new show. Previously he did an hour of stand-up about cooking in hotel rooms, using only a Corby trouser press. Now the DIY cook is in the garden shed using power tools including wallpaper strippers. And he does cook real food during the performance. At the Gilded Balloon Teviot until 27 August (georgeegg.com).

■ Zoe and Layo Paskin, who brought the much-adored Palomar to London from Jerusalem, are opening an English coffee shop called Jacob the Angel in Covent Garden, serving cakes, pastries and pies, mostly for take away, which is helpful. There will only be a dozen seats.

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