Aldi has overtaken Morrisons to become the fourth-largest UK supermarket for the first time, according to data from research firm Kantar.
Discounters are grabbing more market share as shoppers take steps to manage their budgets, Kantar said.
Food prices are rising quickly as energy and fuel costs soar, and the war in Ukraine squeezes grain production and pushes up fertiliser costs.
Kantar said food price inflation hit a record 12.4% in August.
Milk, butter and dog food prices were rising especially quickly.
Inflation in the UK has been rising at its fastest rate for 40 years as food prices climb with living costs eating into household budgets.
"It seems there's no end in sight to grocery inflation as the rate at which food and drink prices are increasing continues to accelerate," said Kantar head of retail and consumer insight Fraser McKevitt.
"Shoppers are taking steps to manage their budgets including broadening the range of stores they visit, with the discount grocers benefiting."
Shoppers are also cutting back on spending by buying more own-brand products, with sales of the very cheapest value own-label products up by a third compared to last year.
Nevertheless, Kantar said food price rises will push up the average annual grocery bill by £571 to £5,181.
Kantar said Aldi's sales rose by almost a fifth in the 12 weeks to 4 September compared with a year earlier, giving it a market share of 9.3%.
Aldi UK and Ireland chief executive Giles Hurley said shoppers were "voting with their feet by choosing Aldi over full price traditional supermarkets".
Meanwhile, Morrisons' sales dropped by 4.1% over the same period, with its market share falling to 9.1%.
Morrisons said market share was "partly a function of new store openings".
"Although Morrisons has not put on any significant new space for a while, some competitors are still opening many new stores," it said.
However, it added that "customers don't really care about market share statistics - they care about value, quality, provenance and service and that is where our focus is going to remain."
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