The seat had become vacant when the constituency's Labour Member of Parliament (MP), Peter Freeman had died on 19 May 1956, aged 67.
He had held the seat since the 1945 general election, having previously been MP for Brecon and Radnorshire from 1929 to 1931.
The Conservative Party selected as its candidate Donald Box, a stockbroker from Cardiff who had contested the seat at the 1955 general election.
Soskice held the seat with a majority higher than that achieved by Freeman the previous year.
He held the seat until he retired from the House of Commons at the 1966 general election, having been Home Secretary from 1964 to 1965.