Monday marks the eighth anniversary of the first renditions to the US concentration camp at Guantanamo Bay.
Almost 200 prisoners are still being held at the base despite pledges from President Barack Obama that the prison would be closed by the end of this month.
To mark the occasion, the 12-year-old daughter of the last Briton to be held in Guantanamo, Shaker Aamer, will hand a letter to Downing Street on Monday afternoon urging Gordon Brown to step up British efforts for the return of her father.
Mr Aamer, a Saudi national and long-term resident in Britain, has been held at Guantanamo since 2002. He was cleared for release in 2007, but his release has been blocked by the US authorities.
There are fears that Mr Aamer's release is being delayed as "punishment" for his role in acting as a representative of fellow detainees at the camp.