Brady first came to prominence as a member of the Independent Labour Party (ILP) in Irvine.
[1] With Patrick Dollan and a number of ILP Members of Parliament, Brady founded the Scottish Socialist Party (SSP), which sought to continue ILP policies while re-affiliating to the Labour Party.
[1] At the 1935 general election, Brady represented the Labour Party in Ayr Burghs.
[2] In order to administer the SSP, Brady had moved to Glasgow, and became involved in the city's politics.
In 1937, he was elected as Secretary of Glasgow Trades and Labour Council, the body at the time serving to represent both the local Labour Party and the city's trade union movement.