Under a pilot scheme launched on Friday, retailers can apply to use the stamp if they pay farmers enough to cover the "sustainable cost of production", which includes a margin for profit and investment.
The year-long scheme is being run jointly by the Soil Association, which certifies organic food, and the Fairtrade Foundation, which encourages ethical trading.
The scheme has received the backing of the Prince of Wales, who said it could encourage "exactly the kind of farming systems we need to see".
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It could be one of the salvations for the small family farm
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Prince of Wales
That kind of farming would value "the freshness, vitality and distinctiveness of locally and regionally produced foods", he said.
It would also improve the relationships between farmers, retailers and consumers.
It could "transform some of the current trading relationships, which so often seem to take place in a climate of fear and mistrust".
The scheme could even be extended to non-organic produce, he suggested.
"It could be one of the salvations for the small family farm, which we need to defend at all costs."
Social contribution
Many UK farmers complain they are financially squeezed by demands for lower and lower prices at the supermarket.
"Many farmers around the world are suffering from prices for their products which do not cover the cost of production, and this is certainly true in the UK," said Patrick Holden, director of the Soil Association.
"The food industry is increasingly dominated by industrial agriculture and trading on global markets," he said.
The group aimed to "tackle how the philosophy and principles of the organic movement can be harnessed to promote socially and environmentally sustainable trading practices."
In developing countries, Fairtrade also provides resources to improve health and education.
UK businesses applying for the new certificate will have to demonstrate that they are making a contribution to social, cultural and environmental development.
This can be through projects such as staff training, encouraging public access to farmland, recycling and composting, and initiatives designed to improve community relationships.
'Good for consumers'
Among the British products expected to be given the Fairtrade mark are potatoes, beef, bacon, lamb and pork.
Organic producers said the new scheme was also good news for consumers.
"Consumers have had no way of knowing... whether the farmer who produced it is getting a fair price, and that the highest standards of social and ethical practices have been followed. Now they will," said Mr Holden.
Fairtrade said that while its focus remained on helping developing countries, it recognised that farmers in the West needed help as well.
Executive director Harriet Lamb said: "This trial with the Soil Association will help us learn how the philosophy and principles of our work can best be applied in the UK context."