Food sales were up on a year ago as the purchase of home-baking products, potatoes and stewing meats were replaced with salads, ice-cream and barbecue foods as the weather improved.
Non-alcoholic beverages, wines, beers and spirits also sold very well compared with a much cooler May last year.
Despite the apparent arrival of summer lifting shoppers' spirits, the underlying trend of customers searching for good value continued, the BRC added.
Online, mail-order and phone sales of non-food items also showed stronger growth, up 12.4% against growth of 10.4% last year.
More top news
Mr Trump’s former national security adviser writes in a forthcoming book that Mr Trump told him he wanted to withhold aid from Ukraine.
The EU chief Brexit negotiator said border checks will be ‘indispensable’.
In the latest part of our series "The Conversation", Ben Chapman has been to north London where three quarters of people voted to Remain.