I have always believed that the secret detention sites – where prisoners were waterboarded – and military prisons, such as Bagram, were far worse than Guantánamo. Now I'm not so sure. They once called it "asymmetrical warfare" and a "good PR move" but the US administration may soon have to call the alleged suicides of prisoners in Guantánamo something they were trying to hide all along: murder.

The latest revelations in the US magazine Harper's suggests a major cover-up occurred after the 2006 deaths of three Guantánamo prisoners: Manei al-Otaibi and Yasser al-Zahrani from Saudi Arabia and Ali al-Salami from Yemen. Four Camp Delta Military Intelligence guards, including a decorated sergeant, have furnished an account dramatically at odds with the official US version of what happened on the night of the deaths. I remember at the time how none of the former prisoners believed the official US version and, after I spoke to the families of the deceased, they too remained convinced that their loved ones had either been killed accidentally or – more likely – murdered.

Last week Johina Aamer delivered a letter to Gordon Brown, asking him to press the US government for the release of her father, Shaker Aamer, who has been held in Guantánamo for more than eight years without charge.

Shaker is regarded as one of the most influential prisoners in Guantánamo because of his vociferous and passionate advocacy for prisoners' rights. As a result of this he has spent many years in isolation, on hunger strike and been forcibly fed liquid food through tubes in his nostrils. At the time of the deaths Shaker told his US attorney, Zachary Katznelson, that he was "strapped to a chair and fully restrained at the head, arms and legs", and that they "cut off his airway, then put a mask on him so he could not cry out". This is similar to what the Harper's article claims happened to the three men before they died. Shaker has also alleged that his head was repeatedly slammed against a wall in Bagram in the presence of at least one British intelligence officer.

Obama's 22 January 2010 deadline to close the prison camp at Guantánamo has not been met. Few of the scores of former prisoners I've spoken to over the last year ever believed it would. The recent problems in Yemen and claims of "recidivism" by some of the former prisoners has become the latest excuse in not releasing the men – not even the hundred or so who have been "cleared" for release. Shaker Aamer was cleared for release over two years ago.

The irony of some of the resettlement cases couldn't be starker. For example, the Uighurs – Muslims from western China – have been resettled in places such as Albania, Bermuda and the Pacific island of Palau: men who have suffered detention without trial, torture and abuse cannot be returned to their homes due to the fear of being detained without trial, tortured and abused.

There are around 50 men, all cleared for release by the US administration, who are unable to return to their countries for fear of torture and execution by states such as China, Libya, Tunisia and Algeria. The US administration has recognised this for many years but releasing them is a major problem. Where will they send them? After eight consecutive and torturous years of demonisation, labelling them "enemy combatants", "terrorists", "murderers" and "the worst of the worst" how could the country so collectively traumatised by the events of 9/11 be expected to simply apologise and say it was mistaken in treating the men like animals?

Instead, the US calls upon the rest of the world to fix the problem it created. Last week I accompanied lawyers for Guantánamo prisoners from Reprieve and the Centre for Constitutional Rights in an effort to help secure homes in Europe for some of the 50. In past months I have met with minsters in Malaysia and Sudan – where the receptions were warm, and the desire to assist in the resettlement programme positive. However, I was unsure how such meetings might be perceived in a place such as Luxembourg. I was pleasantly surprised. Not only did the media cover our visit to the country with references on several of the front pages but the meeting with the foreign minister proved warm. We had a long discussion about the possibility of Luxembourg accepting a couple of the Guantánamo prisoners. He was not unreceptive to the idea and said he would consider the request.

David Miliband has told the Aamer family that Britain is still calling for the return of Shaker Aamer. At the same time, it is believed that the government has documents that contain evidence that confessions he made were obtained through torture, the disclosure of which they are trying to block in court on grounds of "public interest". In light of the torture meted out to Shaker and the deaths that occurred the night he was suffering some of that torture, the public interest seems best served by openness.