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, initially elected Member of Parliament for Bebington in 1970, was unsuccessful in retaining his seat in the 1974 general elections, after a change to the constituency name (Bebington and Ellesmere Port).