Cage's outreach director, Moazzam Begg, is a Briton from Birmingham who was held for three years by the United States government in extrajudicial detention as a suspected enemy combatant at Bagram in Afghanistan, and the Guantánamo Bay detainment camp in Cuba.

[9] U.S. authorities claimed that Awlaki was a recruiter for Al-Qaeda in the Arabian Peninsula, and was involved in the radicalisation of terrorists such as Nidal Hassan, Umar Farouk Abdulmutallab, Zachary Adam Chesser, Faisal Shahzad, and Roshonara Choudry.

[13] At a press conference the following day, Cage's research director, Asim Qureshi, said Emwazi had been "a beautiful young man"[14] and "extremely kind, gentle and soft-spoken".

[15] "Individuals are prevented from travelling, placed under house arrest and in the worst cases tortured, rendered or killed, seemingly on the whim of security agents."

- Cage Prime Minister David Cameron and Mayor of London Boris Johnson both decried the suggestion that Emwazi's radicalisation was the fault of British authorities.

"[2] The Labour Member of Parliament (MP) John Spellar encouraged charities which funded Cage to rethink in light of their recent comments.

[17] An article published in Open Democracy in July 2015 described media response in relation to Qureshi's comments as 'both overwrought and plainly misleading; not to mention a serious dereliction of the journalistic duty to hold power to account.'.

[20] On 25 September 2017, Muhammad Rabbani, the international director of Cage, was found guilty at Westminster Magistrates Court of having wilfully obstructed police at Heathrow Airport by refusing to divulge the passwords to his mobile phone and laptop computer.

In June 2020, a report in The Times had suggested that Cage and Begg were supporting a man who had been arrested in relation to a knife attack in Reading in which three men were murdered.

The Times report also suggested that Cage and Begg were excusing the actions of the accused man by mentioning mistakes made by the police and others.

[23] On 14 March 2024, Michael Gove, Secretary of State for Levelling Up, Housing and Communities, speaking in Parliament, said CAGE was one of five organisations that would be assessed against the new UK Government definition of extremism.

[25] The Trust stated that "We believe (Cage) has played an important role in highlighting the ongoing abuses at Guantanamo Bay and at many other sites around the world, including many instances of torture".