LONDON — Olivier Award-winning British theater director Howard Davies, who had hits in London and Broadway directing Kathleen Turner in “Cat on a Hot Tin Roof,” Lindsay Duncan in “Private Lives,” and Kevin Spacey in both “A Moon for the Misbegotten” and “The Iceman Cometh,” has died. He was 71.

His family said in a statement Wednesday that Davies died following a short battle with cancer.

In Britain he won the coveted Best Director Laurence Olivier Award three times for his work on “The Iceman Cometh,” “All My Sons” and “The White Guard” in 2011. He was nominated for a total of six Oliviers.

On Broadway, he was nominated three times for Tony Awards for his work on Noel Coward’s “Private Lives” in 2002, “The Iceman Cometh” in 1999 and “Les Liaisons Dangereuses” in 1987.

A National Theatre statement called him “one of the very greatest” directors of his generation. He directed a remarkable 36 productions at the National Theatre during a 28-year stretch, beginning with Tennessee Williams’ “Cat on a Hot Tin Roof” in 1988.