Shaker Aamer has admitted he travelled on a false passport as it was the only way he could leave the country.
Him and his wife and children later travelled to Taliban-led Afghanistan using the document.
He said Afghanistan was where they felt "comfortable" as his wife had suffered abuse in the UK because she wore traditional Muslim dress.
A former Attorney General has told ITV News there should be answers to the question of whether British intelligence agents were complicit in alleged torture at Guantanamo Bay.
Lord Goldsmith, who was in the role when Briton Shaker Aamer entered the camp in 2002, said he was "unhappy" that a previous inquiry into the treatment of detainees finished without coming to a "definitive conclusion" over whether detainees were tortured.
In his first television interview, Mr Aamer - who was held in the camp for 14 years - told Julie Etchingham he wants to see an inquiry into allegations of British complicity.
"I hope British agents were not involved or complicit in any way in torture or mistreatment - that's not what they are supposed to do, that's not the British way of dealing with these things," Lord Goldsmith said.
"If the allegations are true, we need to know and they need to be dealt with. If they are not true, the people that were involved, as it were, need to be cleared."
There would be no "great benefit" in conducting an inquiry into allegations made by Shaker Aamer that British authorities knew about torture at Guantanamo Bay, Admiral Lord West has said.
Speaking to ITV News, the former Labour security minister said:
"I'm never convinced about public inquiries, I'm scarred by inquires that seem to go on for years and years and years and cost millions and millions and millions and I don't think achieve much ...
... I'm not sure in this circumstance whether a full judicial inquiry would be of any great benefit."
The chair of parliament's intelligence and security committee has urged Shaker Aamer to submit evidence to its behind-closed-doors inquiry into alleged UK complicity in torture.
Mr Aamer, the last Briton to be released from Guantanamo Bay, has demanded a full public inquiry into the actions of the security services.
In his first TV interview, Mr Aamer told ITV News that British intelligence officers were complicit in his detention and torture.
Former attorney general Dominic Grieve told ITV News the allegations "have to be taken very seriously and we will do so" as he called on Mr Aamer to cooperate with his inquiry.
"It is very much in our interests to look at and find out what happened," he added.
Asked whether former prime minister Tony Blair and former foreign secretary Jack Straw would be called to give evidence, Mr Grieve said: "The committee will decide as it goes along who it calls. I rule nobody in and rule nobody out."
Shaker Aamer has told ITV News he is "scared" the UK security services may "do anything" to silence him since his release from Guantanamo Bay.
Mr Aamer, the UK's last detainee at the prison camp, told Julie Etchingham he felt less secure for "telling the world what happened" to him.
"I really don't want to upset anybody and don't want to start anything in this country that can jeopardise their security," he said.
"But at the same time all I'm doing is telling the truth, that's all."
Tony Blair and George Bush should be given immunity from prosecution in order for the world to learn the truth about claims the US and British were complicit in torture at Guantanamo Bay, Shaker Aamer has told ITV News.
"Accusing governments, accusing individuals is not going to give us the chance to know the truth," he told Julie Etchingham in his first TV interview since being released from the notorious prison camp.
The UK's last Guantanamo detainee said he believed the former British prime minister and US president are both "scared" of being jailed, adding: "How can you expect fear is going to bring justice and bring the truth out of these guys?"
Asked whether he expected Mr Blair would reveal more details about Guantanamo, Mr Aamer said: "If he guaranteed that he's not going to be behind bars I think he would. At least he would be more open about it."
Mr Aamer, who has detained for 14 years without charge, said he believed "nobody should be prosecuted because of what happened in the past" in order to prevent it from happening in the future, saying it would not lead to justice.
A spokeswoman for Mr Blair has said he "never condoned" the use of torture.
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