At the 1945 general election, Blenkinsop was elected as Member of Parliament for Newcastle upon Tyne East. He was Parliamentary Secretary to the Ministry of Pensions (1946–1949) and to the Ministry of Health (1949–1951).
After losing his seat at the 1959 general election, he became a Newcastle City Councillor in 1961. At the 1964 general election, Blenkinsop returned to Parliament as the MP for South Shields, and held the seat until he stood down in at the 1979 general election.
He was President of the Public Health Inspectors Association, a governor of the British Film Institute and vice-president of the Ramblers Association. He became a member of the Medical Research Council in 1965.
- Times Guide to the House of Commons October 1974
- Leigh Rayment's Historical List of MPs
- Hansard 1803–2005: contributions in Parliament by Arthur Blenkinsop