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).

Ellis's big break came in 1975 with his first major role in a popular television series. He played the heart throb Ross Poldark in the BBC 1 series, Poldark.

Ellis co-starred with Lee Remick in the Merchant Ivory film, The Europeans (1979) by Henry James, playing the role of John Acton. He appeared in the CBS mini-series The Curse of King Tut's Tomb (playing Howard Carter, the Englishman who discovered the tomb of King Tut), in the British TV drama, Heartbeat and in a BBC adaptation of A Dark-Adapted Eye (1994) a psychological thriller written by Ruth Rendell.

Ellis had a long career in the theatre as well, including a stint with the Royal Shakespeare Company. He appeared there in a musical version of The Comedy of Errors playing Pinch; in King Lear playing Edmund; Troilus and Cressida playing Achilles; and in Much Ado About Nothing playing Don Pedro. His last West End theatre performance was with Zoë Wanamaker in Sylvia by A.R. Gurney at the Apollo Theatre in 1996.

His cookbook entitled Delicious Dishes for Diabetics: A Mediterranean Way of Eating was published 4 August 2011 by Constable & Robinson, under their RightWay imprint. The American publishers Skyhorse released the book in the United States in November 2011 under a slightly different title, Delicious Dishes for Diabetics: Eating Well with Type 2 Diabetes.

His second cookbook, Healthy Eating for Life, came out in January 2014 in the UK and in March 2014 in the USA. His third cookbook, Mediterranean Cooking for Diabetics: Delicious Dishes to Control or Avoid Diabetes was published in 2016 by Little, Brown UK.