Talks are under way that could allow online grocery shoppers to only buy British products, a minister has said.
Environment minister George Eustice said he was talking with the National Farmers' Union (NFU) about the labelling system for food online.
Tory MPs urged the Government to introduce a button to press while food shopping online "so that you can just choose from British products".
The comments came during a Westminster Hall debate on the future of food labelling, where Mr Eustice also said ministers were looking at using trademark laws to improve the labelling of Angus beef.
Conservative MP Rebecca Pow (Taunton Deane) said: "I would like to raise the subject of labelling on online shopping, because often if one wants to shop online one doesn't know whether it's British food or not.
"Would there be a way that we could consider having a button to press when you do your online shop so that you can just choose from British produce?
"Surely that's really going to help us as we leave the EU?"
Fellow Tory Julian Sturdy (York Outer), who led the debate, said: "I applaud that and I think it's an excellent idea, and I hope the minister certainly takes that point on board."
At the end of the debate, Mr Eustice said: "She raised the issue of online shopping.
"Just briefly, I can say that we are discussing this with the NFU and it may be one of the ways that we can avoid voluntary principles."
Environment, Food and Rural Affairs select committee chairman Neil Parish raised the issue of Angus beef.
He said: "There is a very big chain in this city and others which sell Angus beef.
"Now, I suspect that beef is not Aberdeen Angus from either Scotland or the rest of the United Kingdom, but I suspect most of it is South American Angus beef.
"But because they label it as Angus beef, a lot of people eating it I suspect think it's home-grown Angus beef."
MPs also raised concerns about supermarkets setting up "fictitious" brands that imply the products are produced by UK farms.
Mr Parish and Mr Sturdy were among those to call for clearer food labelling after Brexit to reflect Britain's higher animal welfare standards.
Mr Eustice said he wanted continuity after Brexit but would like to see improvements in the long term, such as mutual recognition for food names that are currently protected.
He said: "We're looking at whether we could use trademark regulations to look at whether we could develop brands in other areas.
"(Mr Parish) mentioned the issue of Angus beef.
"There's another issue with Angus beef, which is it's not always pedigree Angus, or indeed rarely pedigree Angus, it's usually crossed with a dairy animal, and we have the opportunity through trademark regulations and other intellectual property law to develop brands around pedigree beef breeds, native beef breeds, for instance, and we are looking at that."