At the 1922 general election, Alpass was an unsuccessful candidate in the Thornbury constituency in Gloucestershire. He was beaten again at the 1924 general election in Cirencester and Tewkesbury, where the Conservative candidate won 72% of the votes.
At the next general election, in 1929, he was elected as Member of Parliament (MP) for Bristol Central. He was defeated at the 1931 general election, and did not stand for Parliament again until the 1945 general election, when he was elected as MP for Thornbury. He served only one term, until the constituency was abolished in boundary changes for the 1950 general election.
He was born on 2 February 1873 at Clifton in the City of Bristol, but from the time of the 1881 census until at least 1920 he lived in Berkeley where his mother and father ran a grocer's shop in which he worked along with his brother and sister. After the First World War he is recorded as an auctioneer living in Berkeley but also appears to have done business in the Thornbury area. He married Louisa Anne Taylor Neale, daughter of a Berkeley farmer, on 13 September 1905.
- Hansard 1803–2005: contributions in Parliament by Joseph Alpass
|Parliament of the United Kingdom|
| Member of Parliament for Bristol Central
1929 – 1931
Sir Sir Derrick Gunston, Bt.
| Member of Parliament for Thornbury
1945 – 1950