[3] After early stage work with Joan Littlewood's Theatre Workshop, Sutton became known for his unusual roles in two films directed by Sidney J.

[6][7] On stage, he played the title role in the original production of Joe Orton's Entertaining Mr Sloane (1964), and transferred with it to Broadway the following year.

[7][8] From 25 May 1966, he appeared in Tango, a play by Slawomir Mrozek at the Aldwych Theatre alongside Patience Collier, Peter Jeffrey, Mike Pratt, and Ursula Mohan under director Trevor Nunn.

[9] Sutton appeared in many films during his career, including Rotten to the Core (1965), Crossplot (1969), The Devils (1971), Madame Sin (1972), The Pink Panther Strikes Again (1976), Fellini's Casanova (1976), Edward II (1991), and The Football Factory (2004).

In 2003, Sutton starred opposite Edward Hardwicke in David Bartlett's film The Goodbye Plane, and in 2004, he made an appearance in the soap opera EastEnders for sixteen episodes, playing Wilfred Atkins, a conman.

From that statement, he developed a comic piece about "a young man's emotions and feelings, from the moment he's a baby tugging at his cock onwards."

[7] Following a performance as William Blake in Peter Ackroyd's BBC television series The Romantics, Sutton joined the cast of Albion Rising at St Giles in the Fields Church, London, in April 2007.