Market researcher Kantar said total UK grocery sales rose just 0.3% in the 12 weeks to Jan. 26, with the traditional "big four" supermarket groups all seeing year-on-year sales declines.
"Many people start the year with good intentions and pledges to make healthier choices following the excesses of the festive period," said Fraser McKevitt, head of retail and consumer insight at Kantar.
The researcher said No. 2 player Sainsbury's, which last month named a new CEO, was the least worst performer of the big four with a sales decline of 0.6%.
"While still declining, Sainsbury's performance is improving, and online sales were a bright spot – growing by 7% year on year," said Kantar.
Industry leader Tesco, Walmart-owned Asda and Morrisons saw sales falls of 0.9%, 2.2% and 3.0% respectively.
All of the big four continued to lose market share to German-owned discounters Aldi and Lidl, whose sales rose 5.7% and 11.1% respectively, giving them a combined market share of 13.8%. Unlike the big four they are continuing to open lots of new stores.
Kantar said online supermarket Ocado was Britain's fastest growing grocer, with sales up 11.2%.
Shares in Sainsbury's were up 1.1% at 0906 GMT, Tesco was up 0.7% and Morrisons was up 1.2%. The FTSE 100 index was up 1.5%.
Last month, Tesco, Sainsbury's and Morrisons all reported subdued Christmas trading, blaming a tough consumer backdrop.
Kantar said grocery inflation was 1.0% over the 12 weeks. Prices are rising fastest in categories such as bacon, sausages and cooked meat, while falling in butter and fresh poultry.
By James Davey