The Brexit vote has had no immediate impact on shoppers' grocery baskets or their price, figures show.
The nation's average shopping basket is 1.4% cheaper than a year ago, and it remains to be seen if the EU referendum result will bring about any price rises this year, according to Kantar Worldpanel.
Figures for the 12 weeks to July 17 show sales were up 0.1% compared to last year.
Market leader Tesco saw sales dip 0.7% year-on-year over the 12 weeks, with its market share falling 0.2 percentage points to 28.3% - its slowest rate of share loss since March 2014.
A 5% increase in the number of shoppers visiting either Lidl or Aldi over the quarter saw Lidl reach a new market share high of 4.5% thanks to a sales increase of 12.5%, while Aldi, whose sales were up 11%, increased market share to a record 6.2%.
Sales at Iceland were up 2.8% year-on-year, The Co-operative increased its sales by 2.1% and Waitrose grew 1.6%, with all three retailers moving up to 2.1%, 6.4% and 5.1% market share respectively.
Sainsbury's sales fell by 1.1%, while newly installed Asda chief executive Sean Clarke saw sales at the grocer drop by 5.6%.
Morrisons' overall market share fell by 0.2 percentage points to 10.7% but its premium own-label lines showed strong growth of 3.8% 0 the best premium private-label performance among the big four.
Meanwhile, rival research group Nielsen said the value of UK grocers' sales fell 2.4% year-on-year over the four weeks to July 16 - the worst figure since the four weeks ending July 19, 2014.
But it blamed the decline on wet and cool weather rather than Brexit.
Mike Watkins, Nielsen's UK head of retailer and business insight, said: "The low point was the week ending July 2, and the weather is having a big impact on the industry at the moment, adding further pressure on sales from deflation and responding to the growth of discounters.
"The brief mid-July heatwave will have helped kick-start sales for the supermarkets, however August is an unpredictable month and, with a deflationary environment, the measure of success for the next few weeks will simply be to keep hold of new shoppers ahead of the 'back to school' promotions in September."
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