Kantar Worldpanel said that a further 26 per cent of shoppers are considering stockpiling although this has not been borne out in sales just yet.
Fraser McKevitt, head of retail and consumer insight at Kantar Worldpanel, said people are hoarding classic food cupboard supplies, such as tinned goods.
"It's the stuff that people can keep. I'm not sure I'd expect to see a big increase in stockpiling until we approach the deadline. There is no clarity yet and no panic at the tills yet."
He said that overall grocery volumes rose by 1.2 per cent in the four weeks to February 24, which means no increase compared with recent months.
"It’s worth noting that hard-to-stockpile fresh and chilled foods made up 39 per cent of the value of the average British shopping basket," he added.
The latest figures from Kantar also showed Asda outperforming its merger partner Sainsbury's, with the Leeds-based firm seeing a 1.0 per cent increase in sales in the 12 weeks to February 24, while Sainsbury's sales fell 1.0 per cent.
Kantar said that Asda and Sainsbury’s now have a potential combined market share of 31.2 per cent as they await the final CMA ruling on their proposed merger.
The two players suffered a major blow last month when the competition regulator said in a provisional ruling that it could block the deal unless the pair sell off significant stores or even one of the brands.
“Asda continued its run of uninterrupted growth since April 2017, increasing sales by 1.0 per cent. Own label lines at the supermarket continued to outperform brands and an increase in the number of online shopping trips helped boost growth overall," said Mr McKevitt.
He said that Asda has invested in its core own label, which is doing very well, as is its premium own label.
"It is trying to make itself different from the other retailers and it's offering a distinctive own label offering."
He added that Asda's online sales are also doing well, driven by click and collect.
Speaking about Sainsbury's weaker performance he said: "There isn't room in the market place for all four big retailers to do well. Sainsbury's is the one that's currently being squeezed.
"Consumers are a little bit more worried about money."
Morrisons' sales rose 0.8 per cent.
“Morrisons sells 43 per cent of its goods on promotion – a higher proportion than any other supermarket," said Mr McKevitt.
"However, the gap is closing – the supermarket sold £45m less through deals than the same period a year ago.
"Promotions resonate with shoppers. It's exciting and they like a bargain."
Tesco performed the best out of the big four, with sales growing 1.3 per cent.
Kantar said all of Britain's big four supermarket chains lost market share in the 12 week period to German-owned discounters Aldi and Lidl.
Aldi's sales rose 10 per cent, while Lidl's rose 5.4 per cent, taking their combined market share to 12.8 per cent.
Analysts at Nielsen reported that growth in shoppers' spending slowed to 2.5 per cent in February from 3.3 per cent last month, with consumers spending less per visit as Brexit causes increased caution.
Mike Watkins, Nielsen's UK head of retailer insight, said: "Over the last four weeks, the average spend per visit has fallen to £16.30 from £16.70 this time last year, down 2 per cent, as a result of the resurgence of 'little and often' shopping behaviour but also due to price cutting by supermarkets."
Nielsen figures for the last 12 week period show Tesco leading with 26.8 per cent market share, followed by Sainsbury's at 14.8 per cent, Asda at 13.8 per cent and Morrisons at 9.8 per cent.