Barny is Barny Stoppard, the 38-year-old second son of Sir Tom Stoppard’s first marriage. Houndsditch was once the site of the moat bordering the wall of the City. The Elizabethan antiquary John Stow observed that it was so called “from that in old time, when the same lay open, much filth (conveyed forth of the City) especially dead dogges were there laid or cast”. Plus ça change, eh?

Now Barny’s Place, which opened in January, serves surprisingly high-quality fast food for breakfast and lunch to nearby City workers. Barny used to work in video production. Then he opened a sausage sandwich stall in Broadway Market in 2004 which lasted for a few months before he returned to his career. Temporarily, as it turned out. The sausages beckoned. In 2006, he opened the first Barny’s Place in the form of a kiosk selling takeaways in Broadgate Circus, which is still there.

The new Barny’s has seating for 40 and it’s quite nicely designed in a robust, industrial sort of way, with exposed piping, rough-cast concrete walls and counters, and utilitarian tables with Formica tops on tubular steel frames.

A big space has been cleared in front of the main serving counter, so it doesn’t feel cramped or oppressive, and the room is dominated by a giant photograph taking up the whole end wall — a sylvan scene, a bend in a river, some stony cliffs, lots of conifers, maybe somewhere unspoilt in Canada?

Further study is invited by a blackboard wall full of improving Barny-texts, carefully chalked up. “Our inspiration is to bring the farmer’s market to the city,” we are told. “We live in the most diverse city.” There’s even a bit of a prose poem on that theme. “A little Columbia? The Elephant and Castle. Crates of giant snails in Dalston? A Thai food festival in a suburban street in Wimbledon? This is a modern Babylon of food right on our doorstep.”

Actually, the menu is pretty basic: just sandwiches and salads. Hold the giant snails. But the food itself is remarkably good, much tastier than at Pret or Leon, which is all you really need to know.

From the serve-yourself salads, butternut squash with charmoula, coriander and pumpkin seeds, accompanied by a little jar of tahini, was delicious, the pleasantly spiced squash thoroughly caramelised but juicy. A salad of rocket and tomatoes with chunks of flavourful mozzarella and slices of salami and a balsamic dressing was all as fresh as could be. These salads are £1.80 each or priced by weight at £1.20 per 100g.

The sandwiches (from £3.90) all come in a crusty Portuguese bun, quickly toasted up, with a rocket salad and a choice of sauces. The fillings include steak, chicken and chorizo. The superbly meaty Italian sausage, freshly cooked and accompanied by plenty of sautéed onions, plus an optional mustardy mayonnaise, really hit the spot and didn’t feel gross afterwards, as, say, many a turbocharged Pret sandwich does.

There’s also a different soup or stew each day, at £3.25 for a regular serving, £4.45 for a large. A beef in beer stew, tried from the kiosk, was splendid stuff, top-quality beef long braised to be meltingly tender in a rich, aromatic sauce with mushrooms, a dish that would have done credit to an ambitious gastropub at three times the price.

Service here combines the appealing feature of not being at all pushy while you dither but then delivering the goods fast once you’ve ordered. The place knows it’s good, cool even. It has that zing that comes from being one of a kind, zealously run, apparently impossible to maintain for long in a chain.

Drawbacks: eating out of a cardboard box, and no booze. Cardboard boxes have never been an elegant alternative to plates, nor disposable cutlery superior to proper knives and forks, even if virtuously made from potato starch so ready to biodegrade it absorbs stains from the food straightaway. There is something faintly dismaying about eating any meal of the day so much in transit as this.

And lunch isn’t lunch without the glass that cheers, as all the great philosophers agree. A freshly made lemon juice, aromatised with some leaves of mint (£1.50), was pleasantly refreshing but not to be compared with a sappy little Gamay, say. Barny’s staff affirm that they don’t have a bring-your-own-drinks policy yet. Tomorrow, perhaps?