Lawyers for Mr Treshman, asked Mr Justice Schiemann, in the High Court, for bail pending an application for judicial review. They argued that the Home Secretary's decision to make a deportation order against him was 'irrational and unfair'.
But the judge ruled that judicial review was not appropriate. Mr Treshman, now held at a detention centre for illegal immigrants in Gosport, Hampshire, should appeal to an Immigration Tribunal. There was no reason why he should be treated differently from others challenging immigration decisions.
Mr Treshman was arrested on Monday night at BBC Television Centre in west London. The Home Office said his presence in Britain was 'not conducive to the public good'.
Rescue America has been blamed for disturbances and violence in the United States. One of its supporters was charged with shooting a doctor during a protest outside a clinic in Florida. Twenty people were arrested when its supporters and pro-choice groups demonstrated outside the International Planned Parenthood Federation in London on Tuesday.
Jonathan Crystal, for Mr Treshman, 49, said his client's aim was 'to further the debate in this country as to whether abortion should remain lawful'. It was a fundamental basis of democracy that he should be free to do so. Ian Ashford-Thom, for the Home Secretary, said Mr Treshman would not have been allowed to enter the country if the appropriate measures could have been taken in time. He had entered through Gatwick airport as an ordinary tourist. He then took part in a broadcast on BBC Radio 4's Today programme, the contents of which were 'disquieting'.
David Alton, a Liberal Democrat MP, has complained to Kenneth Clarke, the Home Secretary, about Mr Treshman's arrest. He said he did not support Rescue America's tactics but thought the arrest breached principles on freedom of speech.
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