From 1954 to 1955 she was a member of the Old Vic theatre company, appearing in Henry IV and Richard II, and was married for a few months in 1954 to actor Denholm Elliott, whom she met on the set of The Cruel Sea. Their marriage ended owing to his affairs with men. In 1957, she married actor Bill Travers, with whom she had four children and to whom she remained married until his death in 1994.

She and Travers were reunited in Passionate Summer (1959), then she had a support part in MGM’s The Wreck of the Mary Deare (1959). McKenna and Travers were also in Two Living, One Dead (1961), shot in Sweden. She was in an adaptation of A Passage to India for the BBC in 1965.

McKenna has also been responsible for helping create and furnish the Gavin Maxwell Museum on Eilean Bàn, the last island home of Maxwell, an author and naturalist, most famous for his book Ring of Bright Water. McKenna and husband Bill Travers starred in the 1969 film adaptation of the book.

In 1975 she released an album of twelve songs called Two Faces of Love, which included two of her own compositions and a sung version of the poem “The Life That I Have” from the film Carve Her Name with Pride. The record was released on the Gold Star label with two line drawings of McKenna by her sister-in-law Linden Travers, but these were replaced by a photograph when the album was reissued on the Rim label in 1979.

On the stage, in 1979 she won the Olivier Award for Best Actress in a British musical for her performance opposite Yul Brynner in The King and I. Over the years she appeared in more films but was also very active with television roles and on stage where she continues to make occasional appearances.

McKenna appeared in An Elephant Called Slowly. The film features her close friend conservationist George Adamson and also elephants Eleanor (brought up by conservationist Daphne Sheldrick) and young Pole Pole. The subsequent premature death of Pole Pole in London Zoo led to McKenna and her husband to establish Zoo Check in 1984 with their eldest son Will Travers. Zoo Check was renamed Born Free Foundation in 1991. In 1984 McKenna was involved with a protest against the poor conditions at Southampton Zoo which was closed a year later.

McKenna was made an Officer of the Order of the British Empire (OBE) in the 2004 New Year Honours for services to wildlife and to the arts. Her autobiography, The Life in My Years, was published by Oberon Books in March 2009.