Alexis Kanner was born in Bagneres de Luchon, France, to a family of displaced Jewish refugees. They emigrated to Montreal, Canada in 1944. After attending McGill University and performing at the Stratford Festival of Canada, Kanner returned to Europe to pursue his acting career.
In 1959, he joined the Birmingham Repertory Theatre, where he appeared in productions such as The Tempest, Rashomon, and The Naked Island. He also performed at the Dublin Gate Theatre and the Royal Court Theatre in London.
Kanner won acclaim for his one-man performance as Sammy in Ken Hughes' play at the Arts Theatre in London. He also appeared in several films, including The Ernie Game, Crossplot, Connecting Rooms, and Goodbye Gemini.
In the late 1960s, Kanner met Patrick McGoohan, the creator of the cult television series The Prisoner, and appeared in two episodes of the show. He and McGoohan became lifelong friends.
Kanner continued to act in films and television, including the thriller Kings and Desperate Men, which he produced, directed, co-wrote, co-shot, and edited. He also developed several projects for the screen, including Mario and the Magician, Flying Colors, and Picture Yourself.
In the 1990s, Kanner became disinterested in the deal-making part of the filmmaking process and focused on writing prose. He eventually returned to the stage, adapting George Buchner's play Woyzeck, which he was editing at the time of his death.