Heart charter flights could follow as the benefits of British health care become more widely known in the United States.
A private hospital in Surrey has signed one of the first contracts with three US health insurers to do bypass and heart valve surgery at about half the cost of American clinics.
Test-tube baby treatment for American couples is the next British treatment expected to be offered.
Dan Pearson, the middle-man who is linking the British hospitals with the American insurers, said: 'We are right at the start, working at present in the private sector. But I see no reason why the insurers should not also work with the NHS, if the hospitals have the capacity.'
The packages being arranged include travel and accommodation for a spouse or friend. It was too early, he said, to arrange charter flights but he has been in discussion with the airlines and has had a good reaction over possible deals, as numbers grow.
Mr Pearson and his wife, Patricia, Anglophiles from Texas, are working from the offices of Consolidated Communications, a British marketing organisation. They say that a British heart operation costs about pounds 6,000 compared with dollars 25,000 (pounds 17,200) and in vitro fertilisation about pounds 1,200 compared with dollars 10,000 (pounds 7,000) per treatment.
Earlier attempts to reach the mass US market by British hospitals have largely failed. Mr Pearson said: 'The contacts were between doctors and it was not in American doctors' interests to send their patients here. But response from American insurers is quite different.'
Mrs Pearson said: 'British health care offers the best value for money anywhere in the world, and the American health system has very big problems. Americans love the idea of coming to England and especially to be close to London and to stay in these beautiful hospitals in the countryside.'
The infertility market is promising as three American states have ruled that insurance companies must offer four attempts at assisted conception for couples insured with them.
St Anthony's Hospital, Cheam, will provide the cardiac surgery and the Bourn-Hallam Group with centres at Bourn Hall, near Cambridge, and in London, has started to negotiate fertility treatment contracts.
St Anthony's, which has 87 beds, conducts about 500 bypass or heart valve repair operations a year. Philip Cook, marketing manager, said: 'The American insurers can save about dollars 10,000 per patient and if we took two patients week that is dollars 1m saved a year. But I am sure we will take more than that.'
Peter Goldsworthy, managing director at Bourn Hall, said: 'The current position is that we are in early discussions with a high degree of interest.'
One possibility is having their own specialist in America who will diagnose couples and start infertility treatment.