Two years later he transferred into Her Majesty's Customs and Excise, and rose steadily through the ranks to finish as a Higher Executive Officer.
He was active in municipal affairs, and was elected as a Labour Party councillor to Walthamstow Borough Council in 1929.
From 1959 to 1964 Redhead served as an Opposition Whip, and when Labour came into government, he was Minister of State at the Board of Trade.
In October 1965 he transferred to the Department of Education and Science, retiring due to ill health in January 1967.
The resulting by-election came at an inconvenient time for the Labour government, and the Conservative candidate Frederick Silvester gained the seat.