There is a constant hum in the empty dining room above the Ten Bells pub in London's East End. It's before 10 in the morning, the heating isn't on, and the cold from outside bites through the walls. James Lowe, one of the chefs who operates under the Young Turks banner, identifies the problem. It's their reservations phone, which is hiding under a chef's apron slung on to a table. He places it on a pile of soft napkins, where it continues to buzz away. He looks at his fellow Turk, Isaac McHale, and giggles. "We'll get to it," he says.

Lowe and McHale are just over a month into their stint at the Ten Bells, a Victorian pub opposite Spitalfields church, once best known for its links to the Ripper murders but now a fashionable local hangout. Formed in 2010, the Turks were a trio until recently when third member Ben Greeno became head chef at Momofuku Seiobo, David Chang's new restaurant in Sydney. Lowe, 32, was head chef at St John Bread & Wine and has also worked month-long stints at the Fat Duck and Noma; McHale, 31, was the development chef at the Ledbury and was at Noma at the same time as Lowe. Now they're keen to strike out on their own.

In practice this has meant making their name through pop-ups. The first was in November 2010 at the Clove Club, a 24-cover venue in Dalston. They did another four nights last February, because "people kept asking when we were coming back". Next was a six-day stretch – extended due to demand – at Nuno Mendes's Loft Project, an east London supper club that leans towards the experimental. In August they took over Frank's Cafe, on the top of a multi-storey car park in Peckham for two nights. "It was the perfect way to get noticed quickly," says Lowe. "We were dying to just start cooking. But you have to be a more creative chef, to adapt a menu to a space."

Now the Young Turks have extended their two-month run at the Ten Bells (it finishes at the end of February). It's the longest they've spent in one place. "Isaac and I share the same ideals about cooking," says Lowe, "which is to pare things down, to use as few ingredients as possible to create clean-tasting, flavourful food. That means produce has to be brilliant, naturally, and being here for a while has meant we can strengthen our relationships with suppliers we trust."

With a strong emphasis on foraged foods such as mulberries, damson, fennel blossom and pine, the Nordic influence is obvious and there are traces of St John in the emphasis on Britishness. One of the standout dishes from the Loft Project – Jersey Royal potatoes, monk's beard (a marsh vegetable), and Dorset crab – exemplified their approach; simple, with strong flavours, and belying the work that's gone into it.

The hit-and-run tactics might be a fast, relatively low-cost way to get noticed, but they bring their own problems. Money remains an issue, forcing them to fall back on credit cards, overdrafts and "arrangements with venues". At the Ten Bells the rent is paid by wine sales and the fixed-price menu helps with budgeting. But why not concentrate on a permanent opening? "We haven't found the perfect space, or backer," says Lowe. "Everyone we talked to about getting our food out there just said for us to get somewhere open."

Which isn't to say they're not as serious about what they do as anyone following a more familiar path to success. Although, McHale adds, some chefs say, "'What are you two jokers up to now?' like it's a whimsical project."

Lowe pauses. A nerve has been hit. "I think that's one of the most important things for us, to be taken seriously by our peers. We're good enough to be."

While some might be sniffy, other chefs are thrilled. Petter Nilsson has invited them to cook at a festival at his experimental Paris restaurant, La Gazzetta, in March. The Turks will plan and cook a dinner with Nilsson, then conduct a masterclass.

The Young Turks are exciting chefs with a distinctive talent and, for their growing band of followers, not knowing quite where they'll finally end up is part of the fun. They want to do things the "proper" way eventually but, for now, they're living in the moment, and creating one all at once.

The Young Turks are at the Ten Bells until the end of February; 07530 492 986, reservations@tenbells.com