A majority (62 per cent) believe Brexit has had a negative impact on food prices in the supermarket and the broader cost of living (60 per cent), the BMG Research for i showed.
A large number of Leave voters also believe leaving the EU has contributed to surging food costs (42 per cent), and the cost of living (36 per cent), although many also believe it has had no impact on supermarket prices (39 per cent) or inflation (43 per cent).
In figures that put further pressure on Rishi Sunak, more Tory voters believe Brexit has had a negative impact on food prices (48 per cent) and inflation (42 per cent) than those who think leaving the EU has made no difference (34 per cent and 40 per cent respectively).
It comes after the Prime Minister’s nascent plans for a voluntary price cap on food basics in supermarkets were criticised by the industry and some senior Tories this week.
The move, likened to Tory ex-PM Edward Heath’s 1970s price controls, illustrated how Mr Sunak is struggling to get a grip of the cost of living crisis amid stubbornly high price rises for food.
Responding to reports of a potential supermarket price cap this week, the Food and Drink Federation partly blamed Brexit-related factors for high prices, highlighting “friction at the UK’s borders and persistent labour shortages”, alongside separate concerns about recycling regulation.
The Government is nonetheless pushing ahead with the introduction of full border controls and customs checks for EU food imports from 31 October, after delaying them last year to help ease the cost of living.
Robert Struthers, head of polling at BMG, said: “Nigel Farage said Brexit has failed, and it appears the public largely agrees.
“In not a single policy area do we find more of the public saying our EU exit has had a positive than negative impact.
“And on the issue that is probably hitting most Britons the hardest in the pockets at the moment, the cost of the food at the supermarket, the impact is the worst of any of the areas listed.
“As many as six in 10 say the effect of Brexit has been negative here, with only one in 10 positive.”
i reported this week that ministers believe food inflation may have peaked after it fell to 15.4 per cent in the year to May (down 0.2 per cent from April), according to a survey by the British Retail Consortium (BRC) and Nielsen.
But food prices continue to rise at an eye-wateringly high rate.
The BRC figures suggested a person who spent around £20 in a food shop a year ago would now be paying a little over £23 for the same items.
The official Consumer Prices Index food measure for April stands at 19.1 per cent.