Like-for-like sales rose by 3.2% compared with March 2014, according to the survey by the British Retail Consortium (BRC) and KPMG.
That was the strongest growth since January last year.
However, the period covers the five weeks to 4 April and was flattered by pre-Easter trading.
Total food sales recorded their strongest growth since July 2013 with a 1.8% rise as shoppers stocked up ahead of the Easter break.
However, on a like-for-like basis, food sales fell by 0.4% compared with March last year.
David McCorquodale, KPMG's head of retail, said there were signs of recovery in the grocery sector.
However, he added: "Price deflation continues to dog the sector, and while supermarkets may be selling more, they are pedalling hard to stand still. There is a long way to go before like-for-like food sales are back in positive territory."
The increase for March was the third consecutive month of higher retail sales, and followed a fall in December. Like-for-like sales were up 0.2% in both February and January.
The March numbers also showed that physical stores contributed more to growth than online sales for the first time since August - on a three-month average basis.
Furniture and household appliances provided the second-highest contribution to the rise in retailing, helped by the booming housing market.
Colder weather than in the same period in 2014 meant that clothing sales were subdued last month, particularly for womenswear, as buyers left spring and summer ranges on the racks.
BRC director-general Helen Dickinson said: "Retailers can also be satisfied with the consumer response to their Mother's Day and Easter offerings, but it is important to note that April figures will be impacted by the absence of Easter this year."
Howard Archer, chief economist at IHS Global Insight, said: "Given the importance of consumer spending to the economy, a solid BRC survey for March following on from the very healthy retail sales in February would be reassuring for hopes that GDP growth held up reasonably well in the first quarter."
According to the most recent Office for National Statistics figures, UK retail sales rose by 0.7% in February compared with the previous month.
Compared with February 2014, sales were 5.7% higher, the ONS said.
Supermarkets are mounting a "slow but steady fightback" as new figures indicated a sharp rise in retail sales last month.