Asda was the only major supermarket to lift its market share in the last three months as the industry wades through its slowest growth for 11 years.
Wal-Mart-owned Asda saw its share of the grocery market rise to 17.1% from 17% a year ago, according to the latest till-roll figures from Kantar Worldpanel.
The other three major supermarkets - Tesco, Sainsbury's and Morrisons - all saw their market shares slip in the 12 weeks to May 25, compared to a year ago.
The big four supermarkets continue to be squeezed between discount retailers such as Aldi and Lidl and upmarket rivals such as Waitrose.
However, pressure on pricing continues across the whole industry, with the supermarket sector growing by just 1.7% over the period, the lowest level for at least 11 years.
Kantar added that inflation in the supermarket sector fell for the eighth successive period to 1.2%, which reflects price pressures from discounters such as Aldi and Lidl.
Tesco, which is expected to report disappointing first-quarter trading on Wednesday, saw its market share decline to 29% from 30.5% a year ago. Its sales during that period slipped 3.1%.
Sainsbury's suffered a market share fall to 16.5% from 16.7% a year ago.
Discount retailers continued to make strides into the grocery market with Lidl hitting a record market share of 3.6% driven by its highest ever year-on-year growth of 22.7%.
Rival Aldi grew 35.9% over the period and retained its record 4.7% market share it achieved during the previous 12-week period.
At the upper end of the market John Lewis-owned Waitrose also kept its 5.1% record market share achieved during the previous 12-week period, growing 6.1% over the year.
Kantar Worldpanel director Edward Garner said: "At Waitrose, managing director Mark Price's tactic of being 'everything that the discounters aren't' seems to have paid off for the retailer."