For many years Leech campaigned against homophobia and for same-sex marriage. In 2013, he ran a campaign calling for homophobic chants at football matches to be outlawed. Leech is often described as the architect of the campaign to pardon Alan Turing, who was convicted of homosexuality and later committed suicide. He submitted a bill calling for a formal pardon, and at the UK premiere of a film based on Turing's life, "The Imitation Game", the producers thanked him for bringing the topic to public attention and securing Turing's pardon. His campaign then turned to acquiring pardons for the 75,000 other men convicted of the same crime. Leech said it was "utterly disgusting and ultimately just embarrassing" that the conviction was upheld as long as it was, and celebrated the posthumous pardon. Leech's campaign gained public support from popular physicists such as Stephen Hawking. In November 2018 after The Bank of England invited members of the public to vote on which figure should appear on the new £50 note, Leech said it should be Alan Turing so as to "serve as a stark and frankly painful reminder of what we lost in Turing" A number of Leech's campaign posters, letters and campaign material went on display at the Manchester Museum of Science and Indsutry after the Bank of England announced Turing as the new face of the £50 note.