Food price inflation accelerated to 1.4% on the year in May, up from 0.9% a month earlier, figures from the British Retail Consortium and Nielsen show.
Prices overall fell 0.4%, as non-food items experienced price deflation of 1.5%.
Overall prices continue to fall on the year, although the rate now is the slowest since November 2013, BRC chief executive Helen Dickinson said.