British domestic intelligence agency MI5 is facing allegations of "outsourcing" the torture of Pak-origin Britons to Pakistan's ISI, after they were detained during counter-terror operations in that country.

Human rights groups and British MPs today called for an investigation into allegations made by four such British citizens of Pakistani-origin, which were detailed by The Guardian on Tuesday.

They also asked British government to explain what steps were taken to ensure suspects were not tortured after they are detained in Pakistan at the request of counter-terrorism officials.

In a letter to the newspaper, Kate Allen, Amnesty's UK director, said: "Complicity in torture is a crime and you don't defeat terrorism by committing further crimes."

The three men had alleged that they were tortured, but last week, a fourth British national had made similar allegations.

He reportedly alleged that British officials had "outsourced" his torture to Pakistan's Inter-Services Intelligence agency in an attempt to extract information about a planned al-Qaida attack against the UK.

Andrew Tyrie, Conservative MP for Chichester and chair of the all-party parliamentary group on extraordinary rendition, said he would raise the matter in the House of Commons.