Total sales grew by 6.6% during March compared to the same month last year, when sales rose by just 0.6%.
Like-for-like sales, which exclude new stores and space, rose 4.4%.
Total food sales were boosted by shoppers stocking up on Easter treats and meals, up 4.3% in total and up 2.5% like-for-like.
Non-food, non-store sales, which include online, catalogue and phone sales, were 15.9% up on the same month a year ago.
Stephen Robertson, director general of the British Retail Consortium, says the figures are strong but warns the effect of Easter falling in March is “distorting”.
He adds: “In food and drink, this was the most intense March for eight years for promotional activity. Non-food is also a competitive battleground as retailers fight it out to entice customers being put off spending by pre-election uncertainty.”