The decision to stop the donations has already been made by experts advising the US Food and Drug Administration (FDA), who are now considering what criteria to use. They were expected to exclude only long-term visitors to Britain who would have been here during the 1980s, when many BSE-infected cattle were used for food.
Their fears are that visitors to Britain may have absorbed the BSE agent through eating contaminated food, and could then pass on "new variant" Creutzfeldt-Jakob disease (v-CJD) by donating their blood. Potentially, scores of people could be infected by a single donation if it is pooled with others. Because there is no way to detect the BSE or v-CJD agent, thought to be a single protein, conventional blood tests and filtering are useless.
BSE has not been a big issue in the US: no cases of BSE have been officially recorded, nor any cases of v-CJD. But scare stories, and growing publicity such as that by the talk-show host Oprah Winfrey on the beef industry's practices, have pushed it up the agenda.
The authorities now clearly want to head off any crisis of confidence in blood supplies. Ending blood transfusions from people who have been to the UK for six months or more would cut the US blood supply by about 10 per cent.
In 1995 the FDA banned the use of blood products from people with "sporadic" CJD - the form of the disease with no known cause, which usually affects people over 60. But all forms of CJD apparently have a long incubation period in which the victim shows no symptoms: this can last decades before they show failing memory and co-ordination, and die within a couple of years.
In the UK, 40 people have so far died of v-CJD. The Department of Health said last night: "In this country we use leucodepletion, which removes the white blood cells, as a precautionary measure against this theoretical risk. The US's measures are up to their regulatory authorities."
A spokeswoman emphasised that the risk remains theoretical, with no recorded cases of any form of the disease being passed by blood products.
Last night evidence was presented to the FDA's Transmissible Spongiform Encephalopathies Advisory Committee about blood donors who have lived in Britain for various periods, to assess the risk. A study by the US Veterans' Affairs Department found that no one seems to have caught CJD from infected blood.
Abid Rahman, an epidemiologist with the Department of Veterans' Affairs Office of Public Health, said it appears there is only a "small, theoretical risk" of getting it that way. "It at least gives us some evidentiary basis for no transmission through blood so far."
Canadian Blood Services has already decided to refuse blood donations from people who have visited the UK, and has asked an expert committee to decide on the criteria. Because of the close historical ties between Canada and Britain, the decision could have a much more serious effect on Canadian blood supplies.
"The decision to defer donors has essentially been made," Graham Sher, vice-president of the blood services division, said last week. "It's a matter of what the criteria are that we will use to determine who should be deferred."
A survey found that 22 per cent of its donors had visited Britain since 1980.