London (CNN) -- Police are to investigate claims that the British secret services were involved in the rendition of two men to Libya and their alleged ill treatment there, London's Metropolitan Police said Thursday.
The investigation will take place now rather than at the end of a government inquiry into allegations of UK involvement in abuse of detainees, the police said in a joint statement with prosecutors.
One of the cases involves Abdul Hakim Belhaj, a former leader of the Libyan Islamic Fighting Group who became a senior revolutionary commander, while the second is Libyan citizen Saami Al-Saadi, officials confirmed.
"The allegations raised in the two specific cases concerning the alleged rendition of named individuals to Libya and the alleged ill-treatment of them in Libya are so serious that it is in the public interest for them to be investigated now rather than at the conclusion of the Detainee Inquiry," the Metropolitan Police said in a joint statement with the director of public prosecutions.
John Sawers, chief of the British foreign intelligence agency MI6, welcomed the decision in a statement Thursday.
"We will of course be cooperating fully with the police on this new investigation, as we have done on the one now concluding," Sawers said.
"It is in the service's interest to deal with the allegations being made as swiftly as possible so we can draw a line under them and focus on the crucial work we face now and in the future."
A statement from the Cabinet Office said the government would also cooperate fully.
"The government stands firmly against torture and cruel, inhuman and degrading treatment or punishment," it said. "We do not condone it, nor do we ask others to do it on our behalf. The security and intelligence agencies work tirelessly to protect us day in, day out."
The Detainee Inquiry, to be headed by Peter Gibson, was ordered by Prime Minister David Cameron in 2010 but cannot start until all related criminal investigations have been concluded, meaning it may be further delayed by Thursday's decision.
The inquiry's remit is "to look systematically at the allegations about whether British personnel were in any way involved in the alleged mistreatment of detainees held by other countries," following the September 11, 2001, attacks on the United States, its website says.
Last September it confirmed it would look into the claims of British involvement in renditions to Libya.
Clive Stafford Smith, director of the legal action charity Reprieve, also welcomed Thursday's decision by police and prosecutors.
Their statement made clear that "British complicity in the torture of Libyans Sami al Saadi and Abdulhakim Belhaj by the Gaddafi regime is so blatant that a criminal inquiry must go ahead before the government's deeply flawed Gibson Inquiry can get started," he said.
Al-Saadi, also known as Abu Munthir, is suing the British government and intelligence agencies for their alleged complicity in his rendition from Hong Kong to Tripoli in 2004 and subsequent inhuman detention, torture and abuse by the Libyan authorities, according to a letter from his lawyers placed online by Reprieve.
Documents found at Libyan intelligence headquarters in Tripoli by campaign group Human Rights Watch last September highlighted the cooperation between Libya and Western intelligence agencies after Libya ended its weapons of mass destruction program in 2004.
CNN saw an exchange of information between Libyan intelligence and Western intelligence agencies -- such as the CIA, the MI6 in Britain and Canada's intelligence service -- in documents dating from 2004 and 2005. They included a March 6, 2004, CIA letter to Libyan officials concerning Belhaj.
British police and prosecutors also said they would not charge any individuals in relation to allegations of wrongdoing by British officials in two separate investigations, in their statement Thursday.
One, known as Operation Hinton, relates to claims that British intelligence officials were involved in the ill-treatment and torture of Binyam Mohamed, an Ethiopian-born British resident and former Guantanamo Bay inmate, while he was detained in Pakistan.
The other, Operation Iden, was set up to investigate possible criminal wrongdoing after an individual who was detained by U.S. authorities in Afghanistan was questioned by a member of the Secret intelligence Service, or MI6.
Neither investigation produced evidence that would have led to a criminal conviction of an individual, the police and prosecutors concluded.
But, they added, "Nothing in this decision should be read as concluding that the ill-treatment alleged by Mr Mohamed did not take place or that it was lawful."
Stafford Smith welcomed that statement as "the first time any official in any country has conceded that Binyam Mohamed was tortured -- and it is clear from this statement that the CPS accepts that Mr Mohamed was tortured and it was a criminal offense."
It was unsurprising that the authorities had not found evidence to prosecute an individual in the case, he said.
"But the main focus of all this should not be the rank and file, but those who were signing off the torture policy at the top," he added, naming former Prime Minister Tony Blair among them.
The police and CPS have also agreed to set up a panel to look into other claims of ill treatment of detainees and determine whether they should be investigated before the Detainee Inquiry concludes, Thursday's statement said.
CNN's Raja Razek contributed to this report.