Aldi has set out an ambitious plan to conquer the UK grocery market that could see it open up to eight stores in some towns.

“If you look at the population, we think not only could we have a store in every town and city, but for every 25,000 to 30,000 people,” said Matthew Barnes, the UK and Ireland chief executive of the German grocer.

With the UK’s population standing at 65 million that would equate to 2,600 stores – potentially quadrupling the size of the 700-store chain. Tesco currently has 2,700 UK outlets, from small Express shops to superstores.

Aldi had set a target to reach 1,000 stores by 2022 but Barnes told The Grocer magazine the total could be closer to 1,300 by that date, and added: “I think there is massively more potential than that.”

Barnes said: “We have 700 stores now and 300 sites already approved on our books. And there are 600 town locations where we don’t have a store; in many of which we could easily have two, three or four stores … We don’t have a store in Watford, [but] that would be a six to eight Aldi town.”

Aldi opened its first UK store in Stechford, Birmingham, in 1990 but did not become a force to be reckoned with until the last recession, when both it and Lidl won over Britons struggling with their grocery bills at a time when food prices were soaring.

Aldi overtook Waitrose in 2015 and in February moved past the Co-op to become the UK’s fifth-biggest grocer. It is now sitting on a market share of 6.9% – meaning £1 out of every £14 spent in the UK on groceries goes into Aldi’s tills – while Lidl is also making gains. Research group Kantar predicts Lidl could also overtake Waitrose this summer as the discounters benefit from new store openings and shoppers search out bargains amid a return to food price inflation.

Aldi and Lidl are currently the fastest-growing grocery chains in the UK with sales rising at 18.3% and 17.8%, respectively, in the 12 weeks to 23 April, according to Kantar.

Barnes said it would not let British shoppers “fall out of love” with Aldi, highlighting a business model “that enables us to survive off a much lower margin than anyone else”. Last year Aldi reported a second consecutive year of falling profits after the price war it started ate into its own profitability. Operating profit dropped 1.8% to £255.6m in 2015 on sales of £7.7bn. At the time Barnes said it would keep cutting prices to keep them below the likes of Asda, Sainsbury’s, Tesco and Morrisons, even “if losses are an inevitable consequence”.

The scale of shoppers’ defection to the discounters during the last recession forced chains such as Tesco and Morrisons to slash prices, shed staff and offload stores to shore up profits.

Fraser McKevitt, the head of retail and consumer insight at Kantar Worldpanel, said there was plenty of “headroom” in the UK market for Aldi to expand because “a lot of people still can’t shop in an Aldi as their local store”.