Research firm IGD said 17 per cent of people who use convenience stores shop there at least daily, and 59 per cent of these use them at least twice a week.
IGD said on average these shoppers make around three trips a week to a convenience store.
IGD chief executive Joanne Denney-Finch said: "Convenience stores are clearly popular and this trend is set to continue.
"We predict the market will be worth 42.6bn by 2015, up a third from its current value.
"The main consumer trends that will contribute to this growth include a growing population, less meal planning, more people missing meals at home and a desire to shop locally.
"As more and more people live in urban areas nearer convenience stores, retailers and suppliers need to ensure they are aware of the changing profile of their catchment area. And they will have to adapt their product range and merchandising accordingly."
Convenience stores are deemed to be under 3,000 sq ft and open for long hours, every day of the week. Large retailers such Tesco, Sainsbury's and Marks & Spencer have expanded aggressively into convenience in recent years, while Yorkshire rivals Asda and Morrisons stuck to larger stores.
New Morrisons chief executive Dalton Philips said the Bradford-based chain will pilot convenience stores for the first time in 2011. Leeds-based Asda bought 193-store chain Netto UK for 778m earlier this year as part of plans to expand into smaller stores – but not convenience.
Latest industry figures show Asda's share of the grocery market is stagnant, while Morrisons' is slipping.