|Spouse(s)||Diana Quick (1974–1978; divorced)|
Cranham trained at the National Youth Theatre of Great Britain, and at RADA. He starred in the title role in the popular 1980s comedy drama Shine on Harvey Moon, prior to which he had appeared as Charlie Collins in A Family at War (1971). He also appeared in Layer Cake, Gangster No. 1, Rome, Oliver! and many other films. Cranham was cast as the deranged Philip Channard and his Cenobitic alter-ego in the Horror film Hellbound: Hellraiser II. Among many stage credits are West End productions of Entertaining Mr Sloane, Loot, An Inspector Calls (both transferring to Broadway), The Ruffian on the Stair, The Birthday Party and Gaslight (at the Old Vic). For his role as Inspector Goole in An Inspector Calls, he was nominated for a Laurence Olivier Award.
In 2016, Cranham won the Olivier Award for Best Actor in a Play for his role as Andre in Florian Zeller's The Father. The play originated at the Theatre Royal Bath's Ustinov Studio in the autumn of 2014, before touring the country and transferring to the West End in the summer of 2015, returning to the Duke of York's Theatre in spring 2016. The play received an unprecedented five star review from every leading national press publication. Cranham's performance was described as "the performance of his life". 
For BBC Radio 4's Afternoon Play, Cranham played DS Max Matthews in the three-play series The Interrogation by Roy Williams and starred as Thomas Gradgrind in BBC Radio's 2007 adaptation of Dickens' Hard Times.
Cranham was born in Dunfermline, Fife, Scotland, the son of Lochgelly-born Margaret McKay Cranham (née Ferguson) and Ronald Cranham, a London-born civil servant. His first wife was actress Diana Quick. He has two daughters: Nancy Cranham with actress Charlotte Cornwell, and Kathleen Cranham with his second wife, actress Fiona Victory.