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.
Johina, the eldest of Mr Aamer's four young children, will be accompanied by Baroness Helena Kennedy, representatives of Amnesty UK and CND and lawyer Gareth Peirce on the visit to Downing Street.
In a parallel development, legal action charity Reprieve, Amnesty International and former Guantanamo prisoner Moazzam Begg will use the anniversary to call for more European states to accept detainees held at Guantanamo.
It is estimated that around 50 prisoners cannot be returned to their countries of origin for fear of torture or other human rights violations.Â
Reprieve director Clive Stafford Smith and Mr Begg will set out on a tour across Europe on Monday to highlight the situation and urge more countries to act. The trip is being facilitated by Amnesty.
A number of European states have already offered a safe haven to detainees, in line with the stated aims of the EU-US joint agreement on the closure of Guantanamo, but campaigners are urging others to follow suit.
Sharon Critoph of Amnesty International said: "Although several countries have already led the way, it is disappointing that only a few European governments have stepped forward to help those in need of protection.
"Amongst those governments which have failed to assist are those previously most vocal in calling for Guantanamo to be closed."
Along with Bagram airbase in Afghanistan, Guantanamo Bay on Cuba remains a stark symbol of the injustice of the so-called "war on terror."
Human rights groups have expressed concern that the detention facility will remain open past January 22, the date by which Mr Obama had pledged to close it.
Mr Stafford Smith said: "Many European governments have condemned the ongoing detention of prisoners at Guantanamo Bay. Now they can do something about it.
"Actions really do speak louder than words in this case. It's time to turn the rhetoric into reality and get Guantanamo closed as soon as possible."
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