He was a noted treble and sang in Cavan Cathedral, but later would also become a keen member of the school's Gaelic Football squad, representing St Patrick's in the final of the All Ireland colleges competition in 1948.

McKenna had not left the Irish stage behind entirely and would make regular appearances at the Dublin Theatre Festival in A Little Winter Love, Pull Down A Horseman, King of the Castle and Who's Afraid of Virginia Woolf?.

McKenna joined Stuart Burge's company at the Nottingham Playhouse in 1968 playing Trigorin in The Seagull and Sir Joseph Surface in Sheridan's The School For Scandal, both directed by Jonathan Miller.

Later that year McKenna joined the Royal Shakespeare Company and took over the role of Robert Hand in James Joyce's only play, Exiles directed by Harold Pinter.

McKenna returned to the RSC in 1976 for Shaw's The Devil's Disciple, directed by Jack Gold in a production to mark the American bicentennial celebrations, as the revolutionary pastor Reverend Anthony Anderson.

In the late 1980s and 1990s, McKenna returned to the Dublin stage when he was invited by director Michael Colgan to join the Gate Theatre on a number of occasions, including admired productions of Uncle Vanya, The Cherry Orchard and No Man's Land.

He also featured prominently in other television dramas including The Duchess of Malfi (1972), Napoleon and Love (1974), The Changeling (1974), Fathers and Families (1977), Holocaust (1978), the Blake's 7 episode "Bounty" (1978), The Manions of America (1981), To the Lighthouse (1983), The Scarlet and the Black (1983), Bleak House (1985), Strong Medicine (1986), The Play on One: Unreported Incident (1988), Jack the Ripper (1988), Shoot to Kill (1990), TV series Lovejoy - Irish Stew (1993), and the final episode of Inspector Morse - The Remorseful Day (2000).

Other film credits include The Charge of the Light Brigade (1968), Anne of the Thousand Days (1969), Perfect Friday (1970), Villain (1971), Straw Dogs (1971), All Creatures Great and Small (1975), Memed, My Hawk (1984), Pascali's Island (1988), A Caribbean Mystery (1989), Monarch (2000) and The Libertine (2004).

McKenna's wonderfully rich voice featured in over thirty original drama productions for the BBC and the World Service along with readings of short stories and poetry for a variety of programmes.