Market researcher Kantar Worldpanel also said grocery inflation was 2.9 percent in the 12 weeks to Feb. 28, down from 3.6 percent in its last report.
Prices are rising fastest in markets such as butter, fresh fish and fresh pork and are falling in only a few markets, including cooking sauces and laundry detergents.
Kantar said Tesco and Morrisons' sales both increased 2.7 percent year-on-year over the period, ahead of growth of 2.3 percent at No. 3 Asda and 1.1 percent at Sainsbury's.
Shares in Tesco were up 3 percent, Morrisons was up 1.5 percent. However, shares in Sainsbury's were down 1.4 percent.
On Monday Tesco completed its 4 billion pounds takeover of wholesaler Booker.
Kantar highlighted strong growth at Tesco's Extra hypermarkets, and said sales of Morrisons premium own label ranges were particularly robust.
Morrisons held its market share but Tesco, Sainsbury's and Asda all still lost ground to discounters Aldi and Lidl, whose sales rose 13.9 percent and 13.3 percent respectively.
Separately on Tuesday a survey said Britain's shoppers spent more on food in the three months to February and once again cut back on non-essential purchases as the rise in inflation after the Brexit vote of 2016 squeezed their spending power.