MPs are calling for an investigation into allegations that British intelligence has "outsourced" the torture of British citizens to Pakistani security agencies after hearing accounts of people being abducted and subjected to mistreatment and, in some cases, released without charge.

John McDonnell, the Labour member for Hayes and Harlington, and Andrew Tyrie, Conservative member for Chichester, say the allegations should be examined by the Intelligence and Security Committee (ISC), the Westminster body that oversees the Security Service, MI5, and the Intelligence Service, MI6.

In a statement to the Guardian, released via the Home Office, the Security Service insisted it did "not participate in, solicit, encourage or condone the use of torture".

However, details of three new cases have raised concerns among MPs.

McDonnell says he wants to know whether British officials colluded in the abuse of one of his constituents.

The man, a medical student, said he was abducted at gunpoint in August 2005 and held for two months at the offices of Pakistan's Intelligence Bureau opposite the British Deputy High Commission in Karachi. The student, who has not spoken out before, has described how he was whipped, beaten, deprived of sleep, threatened with execution and witnessed other inmates being tortured.

He was questioned about the suicide attacks on London's transport network in July of that year, and says that after being tortured by Pakistani agents he was questioned by British intelligence officers. He was released to his father, who says he received a personal apology from the director of the Intelligence Bureau.

The student returned to his London teaching hospital, qualified last year, and is now working in a hospital in the south-east of England. He remains terrified of both Pakistani and British intelligence agencies, however, and has asked not to be identified. A second Briton, Tariq Mahmood, 35, a taxi driver from Sparkhill, Birmingham, has said he was abducted in Rawalpindi in October 2003 and released without charge about five months later.

He is thought to have been held in a prison run by a different agency, Inter-Service Intelligence, where a number of other Britons have also been held and allegedly tortured before being flown to the UK to stand trial. Mahmood's family say he was tortured, and that MI5 officers and American intelligence officers had a hand in his mistreatment. They have declined to issue any detailed allegation, however, apparently fearing for the safety of relatives in Pakistan.

A third Briton, Tahir Shah, 41, an author from London, was held for 16 days in 2005. He says he was interrogated about the July 7 bombings in what he describes as "a fully-equipped torture chamber", with mangles, whips and electrical equipment.

He says he was hooded and shackled for long periods and deprived of sleep. He does not allege that British officials were involved, but believes it is unlikely they would not have been informed. He was eventually bundled aboard a scheduled flight to Heathrow, where his passport was returned by an unnamed official whom he believes to have been from MI5.

Allegations of collusion in torture could be examined by the Investigatory Powers Tribunal, established eight years ago with a remit to investigate complaints against MI5 and MI6. Another possibility is that the ISC could look into the claims.

McDonnell said of his constituent: "I believe that there is now sufficient evidence from this and other cases to demonstrate that British officials outsourced the torture of British nationals to a Pakistani intelligence agency.

"This warrants the fullest investigation by the ISC, which is best placed initially to undertake such an inquiry. I would expect the government to cooperate fully with such an investigation and eventually for the prime minister to make a statement to parliament on how this practice has been allowed to develop and what action is to be taken."

Tyrie, chairman of the All Party Parliamentary Group on Extraordinary Rendition, added: "Any torture of British nationals by Pakistani authorities would be utterly unacceptable. If credible allegations implicating British officials in such mistreatment have been made then they require investigation. The ISC appears to be the most suitable body to examine these issues."

Asked about the allegations, MI5 asked the Home Office to issue a statement which said: "The government unreservedly condemns the use of torture as a matter of fundamental principle and works hard with its international partners to eradicate this abhorrent practice worldwide.

"The Security and Intelligence Agencies do not participate in, solicit, encourage or condone the use of torture or inhumane or degrading treatment. For reasons both ethical and legal, their policy is not to carry out any action which they know would result in torture or inhumane or degrading treatment.

"The ISC gave the Security Service a clean bill of health in its 2005 report on torture. When Security Service personnel had come across instances when poor treatment of detainees was suspected, the report commended that MI5 officers notified the detaining authorities immediately and this was followed up with an official complaint from London.

"All Security Service staff have an awareness of the Human Rights Act 1998, and are fully committed to complying with the requirements of the law when working in the UK and overseas." Earlier this year representatives of Amnesty International and Human Rights Watch told another Commons body, the Foreign Affairs Committee, they believed British intelligence officers were colluding in torture.

Tom Porteous, London director of Human Rights Watch, told MPs: "It is pretty clear the US and the UK are relying rather heavily on the well-known abusive Pakistani intelligence agency, Inter-Services Intelligence, in the counter-terrorism operations. It is one of the most brutal intelligence agencies in the world." He added that British interrogations of people being held by this agency "seem to amount to complicity and collusion in the mistreatment".

In April the Guardian reported that four other British men, who had been detained in Pakistan during British-led counter-terrorism operations and held illegally for several months without access to a lawyer or court, had each alleged that British officials colluded in their torture.

Under the Criminal Justice Act 1988 it is an offence for British officials to instigate or consent to the inflicting of "severe pain or suffering" on any person, anywhere in the world, or even to acquiesce in such treatment. Any such offence could be punished by life imprisonment.

One of the four, Salahuddin Amin, 33, a university graduate from Luton, later told the Old Bailey that he was interviewed by two MI5 officers several times in 10 months, in between being whipped, beaten with sticks, suspended from his wrists and threatened with an electric drill. MI5 was permitted to give its response to the allegations in camera, with the media and the public excluded.

Allegations of collusion were raised at Amin's appeal against conviction for terrorism offences last month, which was also heard largely in camera. They are to be raised again later this year at the trial of a British man whose lawyers said he had three fingernails extracted while a prisoner of a Pakistani intelligence agency. They say their client was then questioned by British intelligence officers.