McCowen first appeared on stage at the Repertory Theatre, Macclesfield, in August 1942 as Micky in Paddy the Next Best Thing. He appeared in repertory in York and Birmingham 1943–45, and toured India and Burma in a production of Kenneth Horne's West End comedy Love in a Mist during 1945 with the Entertainments National Service Association (ENSA). He continued in repertory 1946–49, during which time he played a season at St John's, Newfoundland, Canada.

He made his London debut on 20 April 1950 at the Arts Theatre as Maxim in Anton Chekhov's Ivanov, and made his first appearances on the New York City stage at the Ziegfeld Theatre on 19 December 1951 as an Egyptian Guard in Caesar and Cleopatra, and on 20 December 1951 as the Messenger in Antony and Cleopatra. Following a series of roles at the Arts and with the Repertory Players, he had rising success as Henri de Toulouse-Lautrec in Moulin Rouge at the then New Theatre, Bromley, and appeared as Barnaby Tucker in The Matchmaker at the Theatre Royal Haymarket, both 1954.

McCowen made his film debut in The Cruel Sea released in 1953. His other film credits include roles in Town on Trial (1957), A Night to Remember (1958), The Loneliness of the Long Distance Runner (1962), The Witches (1966), Alfred Hitchcock's Frenzy (1972), Travels with My Aunt (1972, for which he received a Golden Globe nomination), Never Say Never Again (1983) and Henry V (1989)

After appearances as Dr Bird in The Caine Mutiny Court Martial at the London Hippodrome in 1956, and Michael Claverton-Ferry in T. S. Eliot's The Elder Statesman, first at the Edinburgh Festival in 1958, then at the Cambridge Theatre, he joined the Old Vic Company for its 1959–60 season, among several parts taking the title role in Richard II, then stayed on for the 1960–61 season to play Mercutio in Romeo and Juliet, Oberon in A Midsummer Night's Dream and Malvolio in Twelfth Night.

Television roles included the BBC four-part adaptation of J. B. Priestley's Angel Pavement (1958), and his one-man stage performance of The Gospel According to Saint Mark, transferred to television by Thames for Easter 1979. He appeared in the BBC Television Shakespeare series as Malvolio in Twelfth Night and as Chorus in Henry V, and starred in the lead role of the 1980s TV series Mr. Palfrey of Westminster. His one-man Kipling stage performance was broadcast in 1984, and his later appearances included Albert Speer and Rudolf Hess in the BBC docudramas The World Walk in 1984 and 1985, and the TV series Longitude in 2000.

He joined the Royal Shakespeare Company in September 1962, appearing at Stratford-upon-Avon playing Antipholus of Syracuse in The Comedy of Errors and the Fool to Paul Scofield's King Lear, subsequently appearing in both plays at the Aldwych Theatre in December 1962 – performing these roles again for a British Council tour of the Soviet Union, Europe and the United States from February to June 1964. With the RSC he also played "the gruelling role" of Father Riccardo Fontana in Rolf Hochhuth's controversial play The Representative at the Aldwych in December 1963.

He enjoyed a career breakthrough at the Mermaid Theatre in April 1968 as Fr. william Rolfe in Hadrian the Seventh, winning his first Evening Standard Award as Best Actor for the London production and a Tony nomination after the transfer to Broadway.

At the Royal Court in August 1970, McCowen was cast to play the title role in Christopher Hampton's sophisticated comedy, The Philanthropist. If a philanthropist is literally someone who likes people, McCowen's Philip was a philologist with a compulsive urge not to hurt people's feelings – the inverse of Molière's The Misanthrope. Following enthusiastic reviews the production played to packed houses and transferred to the Mayfair Theatre where it ran for a further three years, making it the Royal Court's most successful straight play. McCowen and his co-star Jane Asher went with it to Broadway in March 1971 where he won the 1971 Drama Desk Award for Outstanding Performance.

He was appointed Officer of the Order of the British Empire (OBE) in the 1972 New Year Honours and raised to Commander of the Order of the British Empire (CBE) in the 1986 New Year Honours.

His next big successes were in National Theatre Comnpany productions at the Old Vic. In February 1973 he co-starred with Diana Rigg in Molière's The Misanthrope for which he won his second Evening Standard award; followed in July 1973 by the role of Psychiatrist Martin Dysart ("played on a knife edge of professional skill and personal disgust by McCowen", according to Irving Wardle reviewing for The Times) in the world premiere of Peter Shaffer's Equus.

McCowen devised and directed his own solo performance of the complete text of the St. Mark's Gospel, for which he received international acclaim and another Tony nomination. It opened first at the Riverside Studios in January 1978 before beginning a long West End season at the Mermaid Theatre then at the Comedy Theatre. Taking the production to New York, he appeared at the Marymount Manhattan and Playhouse theatres.

McCowen published his first volume of autobiography, Young Gemini in 1979, followed a year later by Double Bill (Elm Tree Books).

Christopher Hampton's stage adaptation of George Steiner's novel The Portage to San Cristobal of A.H. at the Mermaid in 1982 gave McCowen a great final speech, an attempted vindication of racial extermination delivered by Adolf Hitler, which for Guardian critic Michael Billington was "one of the greatest pieces of acting I have ever seen: a shuffling, grizzled, hunched, baggy figure, yet suggesting the monomaniac power of the Nuremberg Rallies, inhabiting the frail vessel of this old man's body." It was a performance that also won him his third Evening Standard Best Actor award, a record equalled only by Laurence Olivier and Paul Scofield.

While preparing to co-star as Vladimir to John Alderton's Estragon in Michael Rudman's acclaimed production of Waiting for Godot at the National Theatre in November 1987, McCowen also spent a busy autumn staging Martin Crimp's trilogy of short plays Definitely the Bahamas at the Orange Tree Theatre in Richmond upon Thames, having previously enjoyed Crimp's style of writing in a BBC radio version of Three Attempted Acts. As Charles Spencer wrote in The Daily Telegraph: "As a Director McCowen captures both the subtlety and the richness of these three original and beautifully written plays."

He was the subject of This Is Your Life in 1989 when he was surprised by Michael Aspel at the Strand Theatre in London.

On 2 May 2017 McCowen was accorded a memorial Service at The Actor's Church St Paul's Covent Garden, conducted by the Rev'd Simon Grigg. McCowen's nephew The Rev'd Nigel Mumford read an affectionate remembrance from McCowen's sister Jean Mumford's memoirs titled "Childhood memories of Panto's". The tribute was movingly read by Dame Penelope Wilton, followed by a tribute from the Playwright Christopher Hampton. Rebecca Trehearn sang "Bill" from Show Boat, which was followed by a tribute from the theatre critic Michael Billington and a tribute by the actor Malcolm Sinclair. After final prayers a plaque to McCowen was dedicated by the Rev'd Grigg to the left of the altar.