Jeffrey Steinberg, a US doctor, is offering British couples the chance to choose the sex of their child at his New York clinic. The procedure is illegal in the UK.
Dr Steinberg provoked anger earlier this year when he said his fertility clinic could allow parents to produce "designer babies" - choosing eye, hair, skin colour and gender.
Under American law, he is allowed to use pre-implentation genetic diagnosis (PGD) to reveal an embryo's sex. In Britain, it can only be used in screening for genetic diseases.
Half of the embryos undergoing tests in Dr Steinberg's laboratory reportedly belong to British couples while four more will be tested next month.
"Britain is far more conservative than it used to be. They were the innovators but now they've got handcuffs on," Dr Steinberg said.
"From a business standpoint, it's the best thing going. From a medical standpoint, it's a travesty."
America has allowed sex selection - known by its supporters as "family balancing" - since 2001, but US pro-life groups have criticised the destruction of embryos deemed undesirable.
Earlier this year, the Pope attacked the "obsessive search for the perfect child" and said a "new mentality is creeping in that tends to justify a different consideration of life and personal dignity".
In Britain, officials have warned parents who go overseas for treatment - often after spotting advertisements on the internet - that they should understand the relevant laws and the impact of the selection on any child who is subsequently born.
Other American medical centres have reported receiving interest from British couples, including the Genetics and IVF Institute in Virginia.
The institute said that up to 15 per cent of the 400 PGD cases it handles a year come from abroad. It said it counsels parents before the procedure.
Gary Harton, its PGD scientific director, told The Times that he tells British patients: "You're no different to any other patient. You're here to get what you want. To get a baby."
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