Two terrorist suspects wanted by the United States would be exposed to "a real risk of fundamental injustice and discriminatory treatment" if extradited to America, the High Court was told today.

Babar Ahmad, a computer expert from Tooting, south London, has been accused of running websites inciting murder and urging Muslims to fight a holy war.

Haroon Aswat, a British man arrested in Africa, faces trial on charges of plotting to set up a camp in Bly, Oregon, to train fighters for war in Afghanistan. He has been fighting extradition to the US since being arrested in Zambia and held in the UK.

Today Edward Fitzgerald, QC, appearing for both men, asked two senior judges to halt extradition, arguing there was a danger that their human rights would be abused despite diplomatic assurances from the US Government.

The QC told Lord Justice Laws, sitting with Mr Justice Walker, that the men also faced the risk of extraordinary rendition - the process of removing terrorist suspects to third countries for interrogation - and being held in solitary confinement.

He said that they were in danger of being indefinitely detained under a military order applying to foreign citizens or tried and sentenced by a military commission as enemy combatants in what would amount to "a flagrant denial of justice".

Mr Fitzgerald told the judges that hey should not rely on assurances given by the Americans that the men would be treated fairly.

Both Aswat and Ahmad listened to the opening of their three-day challenge via a video link between the Royal Courts of Justice in London and Woodhill category A prison near Milton Keynes, Bucks, where they are being held.

The cases come to court as the British Government faces mounting pressure over its controversial extradition treaty with the US, which critics say has resulted in a "grotesque injustice" for Britons.

Three British bankers are expected to be extradited to the US later this week under the treaty, on multi-million pound fraud charges connected to the collapse of Enron. David Bermingham, Gary Mulgrew and Giles Darby, known as the Natwest Three, have all failed in their legal bids to have the treaty overturned by the courts.

Conservatives and Liberal Democrats have criticised the "one-sided" nature of the arrangement, which means that British citizens can be extradited to the US without evidence being produced, even though the treaty has not been ratified in the US and there is no equivalent arrangement for the extradition of US citizens to the UK.