Annual food price inflation fell to 5.6% in June, down from 6.4% in May and the lowest rise in 14 months, according to figures from the British Retail Consortium (BRC) out today.
Non-food prices were 1.9% lower than a year ago, which resulted in an overall annual shop price inflation of just 0.7%.
Stephen Robertson, BRC director general, said: "Food inflation is now the lowest it's been for 14 months. That's largely because of falling fresh food inflation, particularly for dairy products and some meats.
"The pound's recent revival is easing the cost of imports and overseas demand for UK produce. Oil prices are up since the start of the year - but are half their peak last July. Food inflation is likely to keep falling."
Mike Watkins, senior manager, retailer services at Nielsen said: "Shoppers are now seeing more savings on their supermarket till receipts as food inflation continues to slow, with the falls in fresh food inflation being most obvious.
"Weak consumer confidence has led to promotional activity being higher in both non-food and food compared with this time last year but the recent good weather has certainly helped shoppers spend again and take advantage of these promotions."
Food price inflation has now fallen for three consecutive months.
Annual inflation in the fresh food category slowed in June to 5.5%, from 6.7% in May. This is the fourth consecutive month inflation has slowed, as downward pressures came from dairy and meat products.
In June, annual inflation in the ambient food sub-category was unchanged from the 5.9% reported in May.
Some of the falls in breads and cereal inflation were counterbalanced by the increase in alcohol prices, partly due to the increase in duty.
Sugar, jams and some confectioneries also increased caused by a 41% increase in the wholesale price of sugar, driven by large scale crop failures.