Britain's Appeals Court ruled in August 2004 that secret tribunals, hearing cases relating to foreign terrorism suspects, could consider evidence that would not be acceptable in a British criminal court.
That meant the authorities could consider information that had allegedly been obtained by torture, provided British agents were not directly involved in any alleged mistreatment.
Civil rights organisations said the ruling was tantamount to legitimising torture.
They described Monday's challenge as momentous in deciding how far the British government could go in rolling back human rights in light of recent acts of terrorism.
"The UK must not accept the unacceptable," said Kate Allen, Amnesty International UK director.
"Torture is abhorrent and can never be condoned under any circumstances."
The Appeal Court's 2004 decision related to the case of 10 foreigners held without charge by Britain under a now defunct law that allowed police to detain terrorism suspects if there were "reasonable grounds" to think they were a threat.
Lord Justice John Laws said torture evidence could be considered by a secretive tribunal, the Special Immigration Appeals Commission (SIAC), that oversaw the men's cases, arguing the 11 September 2001 attacks justified such a stance.
"If [the state] limits the means by which the citizens are protected against the threat of terrorist outrage to the ordinary measures of the criminal law, it leaves a yawning gap," he said.
Amnesty International has
condemned the ruling
"It exposes its people to the possibility of indiscriminate murder committed by extremists who, for want of evidence, could not be brought to book in the criminal courts."
Although Britain uses such information for SIAC hearings, it insists it does not use the US technique known as rendition where suspects are transported to their home countries, where critics say they are sometimes tortured.
Lawyers for Amnesty and the other groups, including Liberty and Human Rights Watch, will make an intervention to Britain's highest court, the House of Lords, on Monday to argue that torture evidence should be prohibited under any circumstances.
"The UK must not accept the unacceptable. Torture is abhorrent and can never be condoned under any circumstances"
UK director, Amnesty International
"This is not about whether evidence is useful. This is about whether the UK will turn a blind eye to someone being thrown in a cell and having pain and terror inflicted upon them," Allen said.
In the wake of the deadly bomb attacks on London in July, Britain said it would deport a number of Muslims whom it described as a threat to national security. The British government has been negotiating with several countries to guarantee such men would not be mistreated.
Those it has held prior to deportation can appeal to the SIAC and can then take their cases through the British courts, with civil rights groups claiming promises of fair treatment from countries such as Jordan were worthless.