Source: Sharecast
According to NielsenIQ, total till sales growth was 4.1% in the four weeks to 6 September, up from 3.7% a month previously.
NielsenIQ said shoppers had shifted focus from summer staples to back-to-school items and early preparations for Christmas.
Promotions were also in demand, as food inflation reached 4.1%, according to the August NielsenIQ-BRC shop price index
Sales of items purchased under promotion increased slightly to 23.5% of sales, with loyalty cards used heavily.
Mike Watkins, head of retailer and business insight at NielsenIQ, said: "Following the hottest summer on record, which encouraged spending and sustained food and drink sales, the industry now faces the challenge of navigating higher inflation.
"One in three households currently identify the cost of living as their top concern, while nearly two-thirds of shoppers report being moderately or severely affected by rising costs.
"Looking ahead, with many shoppers unable, unwilling or reluctant to spend freely, if food inflation reaches 5% or more by the end of the year, this could limit some of the volume increases typically seen during the golden quarter."
The so-called golden quarter refers to the build-up to Christmas, one of most important periods for the retail sector.
Among individual retailers, Tesco saw sales rise 5.0% in the 12 weeks to 6 September, giving it a market share of 26.4%.
At J Sainsbury, Tesco’s closest rival, sales sparked 5.6%.
The online-only Ocado Group reported a 14.3% jump in sales, while discounters Aldi and Lidl saw sales rise 5.2% and 11.4% respectively.
At Marks & Spencer, sales jumped 8.5%.
Nielsen noted that one in four shoppers visited M&S in the last four weeks, an 11.9% improvement in shoppers on last year. It attributed the rise to seasonal food ranges, new store openings and social media engagement.
The total tills data echoed similar research from fellow retail consultancy Worldpanel, released on Tuesday, which also showed both supermarket sales and inflation tracking higher.