Sally Croft, 44, and Susan Hagan, 47, former members of the Bhagwan Shree Rajneesh sect in Antelope, Oregon, decided to fight no further after accusing Michael Howard, the Home Secretary, of pandering to American public opinion.
Their last two High Court applications fell by the wayside yesterday with Lord Justice Steyn and Mr Justice Kay describing them as 'abuses of the legal process'. They said they would not seek leave to appeal against yesterday's ruling either to the Court of Appeal or to the House of Lords.
Five hours after the ruling the women were put on board a United Airlines flight to New York, accompanied by two police guards. Their final destination today is Portland, where the conspiracy was allegedly hatched.
Ms Croft and Ms Hagan left the Rajneeshee community in 1985 but were told in 1990 that they were accused of conspiring to murder Charles Turner, the US attorney who was investigating the sect. Mr Turner was never harmed.
Alun Jones QC, counsel for the women, had argued that Mr Howard had behaved 'irrationally' by refusing to debate their case. He also claimed that the women faced religious prejudice in Oregon, where the Rajneeshees are widely despised.
But, despite the production of highly emotive news footage broadcast in Oregon and a poll showing that 43 per cent of Oregonians consider the women guilty, the judges ruled that there was no risk of prejudice against them.
After four unsuccessful judicial reviews and three applications for writs of habeas corpus, the women decided to fight no more.
'We have a home secretary of so little integrity that we considered it a waste of time to proceed,' said Ms Croft, an accountant from Totnes, Devon.
'He has refused to listen to concerns about the case in the House of Lords and the House of Commons. I feel I have been let down by my country because we don't have a Home Secretary with the courage to break (a) 124-year tradition of extraditing everyone America asks for.'
As soon as the applications fell, Nicholas Parker, counsel for Mr Howard, said the women would be put on an aircraft at 6pm. He opposed granting bail until that time, but his opposition was rejected, allowing the women the dignity of travelling freely to Heathrow airport to present themselves to police.
Ms Croft, accompanied by her partner Malcolm Parlett, and Ms Hagan, with her daughter Katharine, 18, and son Nicholas, 23, travelled by Underground surrounded by a posse of journalists, photographers and cameramen.
''I feel absolutely devastated,' said Ms Hagan, an aromatherapist. 'I have no complaints about the legal process but I do about the way it is hamstrung by political considerations.
'The Home Secretary is supposed to be a safeguard to prevent Britons being sent somewhere where they won't get a fair trial. In this instance, I don't believe we will get a fair trial.'
Both women deny knowing about, or being part of, any conspiracy.
Andrew McCooey, Ms Croft's solicitor, was stunned by the decision to extradite them. 'You could understand it if there was a body, or if a gun was fired, or if someone was in hospital,' he said.
'But nothing like that happened. We're sending two innocent women into a lion's den. There is not a shred of credible evidence against them. We're just ruining two lives to keep the Yanks happy.'
Prosecutors in America have already indicated that they intend to oppose bail for the women. But Lord Scarman, formerly one of the country's most eminent judges, has written in support of the women's applications for bail as part of a growing campaign in support of the women in Parliament.
If convicted, the maximum sentence that can be imposed is life, but American lawyers are predicting the women will get 20 years.