The Wolfenden Report 1957 was one of the key milestones in the struggle to achieve the decriminalisation of male homosexuality
The National Archives site sets out the background history. It provides free access to the full text of some relevant cabinet papers. These include a 1954 paper which argued that establishing a royal commission might lead people to believe that 'the government thought the law ought to be changed ' and result in 'receiving embarrassing recommendations for altering the law'
For a full list of what is available see the detailed search guide on their website
the British Library website also has text from the Wolfenden report and discussion