Nearly eight in 10 believe that imported food should meet UK standards on the environment and animal welfare, a ComRes survey has revealed.
The study, commissioned by the British Guild of Agricultural Journalists (BGAJ), comes as the UK and Australia conclude the last stages of a free trade agreement.
The potential deal has drawn a backlash from farmers, who fear being undercut by cheaper foreign imports, and campaigners, who argue it will mean low-grade food hitting the shelves.
It is the latest in a series of rows about post-Brexit trade deals, the most famous being the controversy over chlorinated chicken in a UK-US agreement.
A third of those surveyed said they only buy food marked with the Red Tractor logo, which ensures that the food is safe to eat and has been farmed responsibly.
Around 55 per cent thought it was important for food to have a low carbon footprint, while 14 per cent disagreed.
Four in 10 claimed they would happily pay more for food with a lower carbon footprint.
The study proved that “the public would not support any free trade deal allowing Australia tariff-free imports on beef, lamb and sugar – an arrangement that would undercut UK farmers,” BGAJ president Baroness Rosie Boycott said.
“The public appreciates the multifaceted work our farmers do on a daily basis and believes our industry still has a pivotal role to play in providing food for the country while safeguarding the environment.
“We can only hope the government feels the same way.”
The study comes after news that the UK intends to reveal its deal with Australia before the G7 summit begins on June 11.