Brooke, the son of a woolsorter, was born in Bradford. He went to Carlton Street Secondary School; his first job was as an office boy for the Amalgamated Society of Dyers. His work for the Society qualified him for a scholarship to the London Labour College where he studied politics and economics.
A bachelor, in 1925 Brooke was elected to Bradford City Council as a Labour Party councillor. He became Chairman of the Governors of his old school, and took a particular interest in 'special schools' for the physically disabled.
At the 1929 general election, Brooke was elected for Dunbartonshire. He lost that seat in 1931, but returned to Parliament in the 1935 general election for Batley and Morley. He suffered poor health from 1938, and stayed at Grassington in North Yorkshire and the Isle of Wight in order to recover, but during the Sudeten Crisis he returned to Westminster.