Overall shop prices reported deflation of 0.4 per cent in April from the 0.5 per cent fall in April.
This is the shallowest deflation rate since November 2013.
Non-food deflation deepened slightly with prices falling 1.5 per cent over the year to May compared to the 1.4 per cent decline in April.
Excluding last month this is still the shallowest deflation rate since May 2013.
Food inflation accelerated to 1.4 per cent from the 0.9 per cent rise in April.
Fresh Food inflation was 1.2 per cent up from one per cent in April. Ambient Food inflation was 1.8 per cent in May from 0.8 per cent in April.
Helen Dickinson OBE, chief executive, British Retail Consortium, said: “Overall prices continue to fall year on year, albeit now at the slowest rate since November 2013. However the trends for Food and Non-Food are now two quite different stories.
“With shorter stock turnaround times, the impact of the weaker pound has already started feeding through into food prices; although food price inflation this month is still well below the input cost price increases being faced by retailers.
“By contrast, heavy discounting in the wake of a weak start to the year and the fact that some businesses are still protected by hedging contracts are keeping non-food prices deflationary for now.”