Food inflation hit a two-year low in July, dropping to 3.1% from 3.5% in June.
Overall shop price inflation slowed to 1%, from 1.1% the previous month, according to the BRC-Nielsen Shop Price Index.
Non-food inflation remained stable at 0.3%.
British Retail Consortium director general Stephen Robertson said: “A two-year low for food inflation is good news for hard-pressed households still suffering falls in disposable incomes. Lower shop price inflation is helping to narrow the gap between living costs and wage increases.
“Extra promotions, particularly linked to party food and this summer’s big events, are combining with past falls in commodity prices which are working their way through to shop prices.”
However, Robertson warned it may not last as poor harvests, especially of corn and wheat in the US, are creating a build-up of inflationary pressure.