Prices rose by 5.7%, speeding up from 5.1% in the 12 months to August, led by an unprecedented 10.6% jump in food prices as the war in Ukraine inflated the costs of animal feed, fertiliser and vegetable oil, the BRC said.
Market research firm NielsenIQ, which co-produces the data, said 76% of consumers expected to be moderately or severely affected by the cost-of-living crisis over the next three months, up from 57% in the summer.
"So households will be looking for savings to help manage their personal finances this autumn and we expect shoppers to become more cautious about discretionary spend, adding to pressure in the retail sector," Mike Watkins, NielsenIQ's head of retailer and business insight, said.
Britain's consumer price index, which measures a broader range of prices than the BRC's data, hit a 40-year high of 10.1% in July before easing back to 9.9% in August.
The cost of imported goods in Britain faces further inflationary pressure after a slump in the value of the pound triggered by the announcement of tax cuts by new finance minister Kwasi Kwarteng last week.
(Reporting by William Schomberg, editing by Andy Bruce)