Shaker Aamer, the last British resident held in Guantánamo Bay – where he has been incarcerated for the past eleven years despite protests from the British government – has spoken from his prison cell for the first time.

"Tell the world the truth … Please, we are tired. Either you leave us to die in peace – or tell the world the truth. Let the world hear what's happening," Aamer told CBS's 60 Minutes show.

Aamer added: "You cannot walk even half a metre without being chained. Is that a human being? That's the treatment of an animal."

Reprieve, the legal charity and human rights group acting for Aamer, said the unique recording, broadcast on Sunday night, probably survived because the US military authorities were concerned that the consequences of censoring America's most powerful news programme would outweigh the embarrassment of allowing him to speak.

Aamer has been held in Guantánamo since 2002 but has not been charged with any offence. William Hague, the British foreign secretary, has many times raised the case with the US administration with no success.

Shaker Aamer, the last British resident held in Guantánamo Bay, told CBS: 'Tell the world the truth … Please, we are tired.' Photograph: Getty Images

A Foreign Office spokesperson said on Monday night: "Mr Aamer's case remains a high priority for the UK government and we continue to make clear to the US that we want him released and returned to the UK as a matter of urgency. The prime minister raised Mr Aamer's case with President Obama during the G8 in Northern Ireland in June".

The spokesperson added: "The prime minister later wrote to President Obama reaffirming the importance the UK places on the request for Mr Aamer's release. The deputy prime minister went on to raise Mr Aamer's case with vice-president Biden in September. We are confident that the US Government understands the seriousness of the UK's request for Mr Aamer's release. Any decision regarding Mr Aamer's release ultimately remains in the hands of the United States Government."

Aamer has British residency, and his British wife and their four children all live in south London. The US has repeatedly threatened to send Aamer to his birthplace, Saudi Arabia.

Aamer has described how he was tortured at the infamous Bagram jail in Afghanistan in between being questioned by US and British intelligence officials there. According to leaked alleged confessions, while he was in London Aamer was "assessed to be a key member of the UK-based al-Qaida network with multiple associations to senior al-Qaida members". Shaker has denied the claims made about him.

Clive Stafford Smith, Reprieve's director, said: "CBS's show gives a very rare and very shocking glimpse inside Guantánamo Bay. Everyone in the prison – the guards and the men – is suffering horribly, day after day. Obama must fulfil his promise to close the prison and Shaker Aamer must come home to his family in the UK, which is what David Cameron has said he wants."

A US court for the first time has allowed an independent medical and mental health expert of Aamer's choice to have access to the prisoner.

"We're glad the US government agreed in the end that Shaker should be able to see a doctor of his choice after more than a decade in indefinite captivity. We're now looking into next steps," Ramzi Kassem, Aamer's US lawyer, told the Guardian.