Beginning his career as a decorator, Wallhead joined the Independent Labour Party (ILP) and later became a journalist and lecturer.
A committed opponent of World War I, he was detained in 1917 under the Defence of the Realm Act.
Wallhead unsuccessfully contested Coventry in the 1918 general election for the Labour Party, to which the ILP was affiliated.
As the politics of the South Wales coalfield radicalised, this turned into a safe Labour seat, which he was to hold until his death.
His daughter Muriel Nichol was also a Labour politician, and served as MP for Bradford North from 1945 to 1950.