Market researcher NIQ said supermarket sales on a value basis grew 7.2% in the four weeks to 12 August - the lowest growth since January and down from 8.9% in its July data set.
The data is the most up-to-date snapshot of UK consumer behaviour.
NIQ said sales on a volume basis fell 3.8%.
Britain's consumers have largely defied high inflation and rising borrowing costs to keep up their spending in 2023, but July's official measure of overall retail sales showed a fall in sales volumes which was widely attributed to rain.
NIQ said supermarkets, in a bid to encourage demand, edged up spending on promotional activity to 23% of all fast moving consumer goods (FMCG) sales versus 22.5% in the previous month, noting targeted price cuts and loyalty card offers.
The researcher said market leader Tesco saw sales increase 9.7% over the 12 weeks to 12 August, with its market share nudging up to 26.8%.
NIQ said discounters Aldi and Lidl, with sales up 22.2% and 16.5% respectively, and Marks & Spencer, with sales up 11.5%, were the only other grocers who gained market share in this period.
Last week, M&S upgraded its profit outlook.
Mike Watkins, NIQ’s UK head of retailer and business insight, said that despite easing inflation, most consumers remain pessimistic about their financial situation in the coming three months, with 60% anticipating that they will be severely or moderately impacted by rising living costs.
"With the added concerns of increasing mortgage and rental expenses for many households, it appears that a shift in sentiment may be some time off," he said.