Originally elected Member of Parliament for Bebington in 1970, Cockeram lost his seat (which he fought unsuccessfully as the renamed Bebington and Ellesmere Port) in both the 1974 general elections.
Cockeram, who was first elected to Parliament in 1970 for Bebington, lost his seat in both the 1974 general election, which he fought unsuccessfully as the renamed Bebington and Ellesmere Port.