Wymark attended University College London before training at the Old Vic Theatre School and making his first stage appearance in a walk-on part in Othello in 1951. He toured South Africa the following year and then directed plays for the drama department at Stanford University, California.

Wymark married Olwen Wymark, an American Playwright, in 1953. He took his acting name from his grandfather-in-law, the Writer william Wymark Jacobs. The couple lived in Parliament Hill, Hampstead, and had four children, including the Future Actress Jane Wymark. He had a brother, John Cheeseman.

After moving to the Shakespeare Memorial Theatre in Stratford-upon-Avon, Wymark played a wide range of Shakespearean roles, including Dogberry in Much Ado About Nothing, Stephano in The Tempest, Marullus in Julius Caesar and Bottom in A Midsummer Night's Dream. Other stage credits included the title role in Danton's Death and, with the Royal Shakespeare Company (RSC), Ephihodov in The Cherry Orchard. His theatre roles also included Bosola in a RSC production of John Webster's The Duchess of Malfi in 1960.

In television, Wymark was best known for his role as the machiavellian businessman John Wilder in the twin drama series The Plane Makers and The Power Game (which were broadcast from 1963 to 1969), which led to offers of real company directorships and the British Academy Television Award for Best Actor in 1965. However, Wymark was a gentle person in real life and was, by his own admission, ignorant of Business matters. He considered the character of Wilder a "bastard" and was described by his wife Olwen as "the most inefficient, dreamy muddler in the world." In the mid-1960s, Wymark was considered as the replacement for william Hartnell in the title role of Doctor Who.

Wymark's film appearances included: Children of the Damned (1964), Operation Crossbow (1965), Repulsion (1965), Where Eagles Dare (1968), Witchfinder General (1968), Battle of Britain (1969), Doppelgänger (1969), The Blood on Satan's Claw (1970) and Cromwell (1970)

Wymark died suddenly in Melbourne, Australia on 20 October 1970, aged 44, of a heart attack in the hotel room in which he was staying. He had been due to star in the play Sleuth at the Comedy Theatre three days later. On the night of his death, he was to appear on the TV variety programme In Melbourne Tonight. He, guest Richard Deacon and host Stuart Wagstaff had just appeared together in a TV production of Hans Christian Andersen stories, and his non-appearance led to several jokes by Wagstaff and Deacon. Host Wagstaff was informed of Wymark's death mid-way through the programme and announced it at the end.

He was buried at Highgate Cemetery in London. Wymark View—located in his home town, Grimsby—is named after him.