Born in Beckenham, Kent, he became widely recognised as the abrupt, bewildered Mr Walt in the Fawlty Towers episode "The Hotel Inspectors" and as Mr Watson, the frustrated Public Relations training course instructor, in an episode of Some Mothers Do 'Ave 'Em.

Cossins appeared in Charley's Aunt at the Apollo Theatre in 1971 with Tom Courtenay, David Horovitch, Garth Forwood, Joanna McCallum, and Celia Bannerman.

He appeared in more than forty films,[5] including The Anniversary (recreating his West End stage role), and The Lost Continent (both 1968), Gandhi (1982), and The Man with the Golden Gun (1974).

On the small screen, Cossins appeared as a guest in a variety of shows, including The Likely Lads and Whatever Happened to the Likely Lads?, Minder, Bergerac, The Sweeney, Bless This House, Shadows, All Creatures Great and Small, Citizen Smith, Just William, The Good Life, L for Lester, Neville Dennis in Callan "Rules of the Game" (1972), Z-Cars, and as the regular character Bruce Westrop (in 1979) in Emmerdale Farm.

He played a magistrate in episodes of four different British sitcoms, Whatever Happened to the Likely Lads?, The Good Life, Citizen Smith and Minder.