It could had gotten out in 1945-47 when there was apparently pretty strong support by the Foreign Office for union of Cyprus with Greece. In September 1945 the Permanent Under Secretary of Foreign Affairs, Sir Orme Sargent was proposing as much while as late as September 1947 you had Sir Oliver Harvey the Deputy Under-Secretary of State writing that:
“Our proposed evacuation policy in Palestine and the possibility that we may propose independence for Cyrenaica, when coupled with what we have done in India and Burma, makes our continued presence in Cyprus indefensible […] We have in fact never made use of the island for military purposes and we have spent next to nothing on its material and social betterment. We have nothing to be proud of there […] It can hardly be questioned that Greece, who has long governed Crete effectively, and has now been given the Dodecanese, can equally well govern Cyprus. (There is a small Turkish minority whose rights would be secured) […] For these different reasons I would strongly advocate that consideration be given to the very early cession of Cyprus to Greece, before the Cypriot campaign is embittered by violence and before cession can be represented as yielding to force […]"
By 1955 Britain instead was dead set on keeping Cyprus, with frex the Undersecretary of State for the Colonies, Henry Hopkinson. stating in the Commons that, Cyprus could ‘never’ expect to be fully independent.
Source of the quotes from
here