Blenkinsop is a surname of British origin. Notable people with the surname include:
Arthur Blenkinsop, (1911–1979), Labour MP
Christopher Blenkinsop (born 1963), Anglo-German musician
Ernie Blenkinsop (1902–1962), English football (soccer) player
John Blenkinsop (1783–1831), mining engineer and an inventor
Joseph Blenkinsopp (born 1927) British-American theologian and Old Testament scholar
Tom Blenkinsop (born 1980), British politician
Tommy Blenkinsopp (1920–2004), English footballer
Fictional characters:
Bertie Blenkinsop, character in The Beano comic, one of the softies and enemy of Dennis the Menace.