He went to Mill Hill School and then Trinity Hall, Cambridge, before returning to east Lancashire where he became a director of companies involved in the weaving and matchmaking industries in Colne and Rawtenstall.
As the Second World War loomed, Leavey joined up and served in the 5th Royal Inniskilling Dragoon Guards in France and Belgium; he only just escaped at Dunkirk, being one of the last to be evacuated.
He was a strong supporter of the government over the Suez Crisis and attacked nearby Labour MPs for supporting Gamal Abdel Nasser, being rewarded with appointment as Parliamentary Private Secretary to Walter Monckton for one year from 1956 and later to Derick Heathcoat Amory in 1959; however, his loyalty did not stretch to accepting what he saw as government indifference to the local cotton industry.
When his pressure resulted in the passing of the Cotton Industry Act 1959, it was felt to have aided his campaign locally; despite it, in 1962, he was one of five Conservative MPs to support a Labour motion of censure on the subject.
When Prime Minister Harold Macmillan sacked seven members of his cabinet in the "Night of the Long Knives" in 1962, Leavey praised him for being ruthless with colleagues when necessary.