British Prime Minister David Cameron says an inquiry led by a judge will look at claims that British security services were complicit in the torture of terror suspects.
He says compensation will be paid to victims if it is found foreign agents committed abuses with their British counterparts present.
Mr Cameron says Britain's reputation as a country that believes in human rights will continue to be tarnished until the allegations are investigated.
Several Britons of Pakistani descent say they were abused in custody in Pakistan, with British complicity. British authorities say they would never use torture to gain information.