Annual rise of 11.6% comes as milk, teabags and sugar become more expensive.
October was up 13.3% year on year compared with a rate of 12.1% in September.
Non-food inflation picked up to 4.1% from 3.3% the month before, meaning overall shop prices were 6.6% higher year on year.
BRC chief executive, Helen Dickinson, said: “It has been a difficult month for consumers who not only faced an increase in their energy bills, but also a more expensive shopping basket.
Even the price of basic items went up, with the price of the humble cuppa rising, as teabags, milk and sugar all saw significant rises.
While some supply chain costs are beginning to fall, this is more than offset by the cost of energy, meaning a difficult time ahead for retailers and households alike.
Everyone wants to enjoy Christmas but you’ve got to take a view that certainly for the next three to six months we’re not going to see any rapid decline in inflation.
Richard Walker, the managing director of Iceland Foods, also warned of further price rises and growing food insecurity.