Bradford-based Morrisons was the worst performer of the big four supermarkets, according to the latest Kantar figures, although all four saw sales fall.
Fraser McKevitt, head of retail and consumer insight at Kantar, said: "The issue that Morrisons has had for a number of months is that people are putting fewer items in the basket, so its average basket size has been getting smaller and it has been attracting fewer shoppers through the doors.
"So the two of them combined have been a bit of an issue."
However it appears that Morrisons is seeing signs of improvement.
"I would say that in the latest data, although Morrisons is the worst of the big four, we're just starting to see a slight chink of light for it in that it did actually attract about 30,000 more shoppers than it did last year," said Mr McKevitt.
"We always see the number of shoppers coming through the door - footfall - as the most important indicator of a retailer's performance, so the fact that has turned round for the first time in a number of months means that it might be starting to head in a more positive direction."
He said this is probably down to Morrisons' focus on price.
"Morrisons has been shouting about what it is doing on price," said Mr McKevitt.
"In our data, we certainly see it promoting more than it did and promoting more heavily. Morrisons probably don't see what it is doing as promotions as such.
"It sees itself as cutting back on everyday prices so not one-off price cuts, but actually making the price of every day goods cheaper. The message might be starting to get through."
Sales at Leeds-based Asda fell 1.0 per cent over the 12 week period.
Mr McKevitt said: "Asda has had a difficult 12 weeks, like everyone else. Like Morrisons, its performance this month is better than last month, but still not back up to the magical growth line.
"Asda has done quite well in sales of pet food. Crisps and snacks have also been a highlight and its Extra Special range is still growing at 10 per cent year on year. So it is managing to find growth in some isolated places."
The latest Kantar data showed that households are buying fewer grocery items than last year despite speculation about stockpiling ahead of Brexit.
Households bought 0.9 per cent fewer items than the same quarter last year, suggesting people are not stockpiling ahead of Brexit.
Overall, the market welcomed a return to growth despite the political uncertainty, with sales by value increasing by 0.5 per cent over the 12 weeks to September 8.
Lidl gained an extra 618,000 shoppers compared with last year while a third of British households shopped at the Co-op, helping it to increase sales by 1.8 per cent.
Mr McKevitt said: "As we move closer to October 31, it seems talk about stockpiling might be just that because we're not seeing any evidence of it at the moment.
Ocado was again the fastest growing grocery retailer overall as sales increased by 12.7 per cent, with customers buying at least 20 per cent more ice cream, cheese and sparkling wine.