Ellis was born in Ipswich, Suffolk. He and his brothers were educated at the independent Highgate School in Highgate in north London, and at Fitzwilliam College, Cambridge where he read history and appeared in over 20 plays. His first West End performance was in Sheridan's The Rivals at the Haymarket Theatre, as Captain Jack Absolute. He went on to play in The Real Inspector Hound at the Criterion Theatre and Widowers' Houses at the Royal Court. He was part of the innovative Actors' Company, founded in 1972 by Ian McKellen and Edward Petherbridge, organised and run democratically by the actors themselves. In that repertory company he appeared in 'Tis Pity She's a Whore, Ruling the Roost, The Way of the World, The Wood Demon, The Bacchae, Tartuffe, King Lear and Knots (based on the R. D. Laing book).