British domestic intelligence agency M15 is facing allegations of outsourcing the torture of Pak-origin Britons to Pakistan's Inter Services Intelligence, after the accused were detained during counter-terror operations in that country.

Human rights groups and British Parliamenterians 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 the 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.

"Allegations of UK involvement in torture or extraordinary renditions are extremely serious. All such allegations must be properly investigated by the government. The public must have confidence that British officials are not complicit in torture," the newspaper quoted him as saying.

The fourth man is reported to be from the West Midlands, where several arrests had taken place in the recent past. He was quoted as saying that for several months, the ISI kept him in a pitch-black cell not much bigger than a coffin, and that he was subjected to beatings, whippings and electric shocks.

On one occasion, he alleged that he was kept hooded and interrogated by people speaking English, with both British and American accents. The man reportedly made the allegations to family members and to a lawyer in Islamabad who was eventually allowed to see him.

The Guardian report said: "The allegations cannot be corroborated, and Pakistani authorities claim the man's whereabouts are unknown now that he is no longer in their custody."

However, his claims follow similar allegations made by three other British citizens of Pakistani-origin.

The latest man to allege British collusion in his torture was reportedly living in Pakistan for almost four years when he was picked up by the ISI two years ago, during a British-led counter-terrorism operation, the report said.

Shortly after his arrest, the report said that an agency story had an unnamed Pakistani official as saying he had been 'broken' during interrogation. When he was eventually taken from the ISI interrogation centre to a prison, and made to see a lawyer, he said he had been interrogated by westerners as well as Pakistanis, and alleged he had been mistreated.