The actor was lauded for his portrayal of British Olympic athlete Harold Abrahams in the 1981 film, which won four Oscars including best picture.
A statement from his representatives said: “Ben passed away suddenly today following a short illness. He had just finished shooting The Devil’s Light for Lionsgate and later this year will be seen in Last Letter From Your Lover in a leading role.”
A post on his Facebook page, which claims to be written by his daughter Lauren, said Cross experienced a “rapid decline” in the last week.
It said: “I am utterly heartbroken to share with you that my darling father died a few hours ago.
“He had been sick for a while but there was a rapid decline over the past week.
“The press will be announcing his death soon, I just wanted you all, his most loyal and loving fans, to hear it from us first.
“Thank you for all your support over the years. He really enjoyed interacting with you.”
Cross was born Harry Bernard Cross in London to a working class Catholic family.
In 1970, he was accepted into the Royal Academy of Dramatic Arts (Rada) aged 22.
After graduating, he moved from the stage to screen and appeared in a minor role in 1977’s A Bridge Too Far alongside Sir Sean Connery and Sir Michael Caine.
The same year he became a member of the Royal Shakespeare Company and performed in Privates On Parade.
He found wider success in 1978 appearing in the play Chicago as Billy Flynn, the lawyer representing murderer Roxie Hart.
That performance is widely believed to have earned him his role in Chariots Of Fire.
Cross played athlete Abrahams, with the late Sir Ian Holm nominated for an Oscar as best supporting actor in his role as coach Sam Mussabini in the film based on the true story of two British men racing for Olympic gold in 1924.
In the intervening years, he appeared as Malagant in 1995’s First Knight and Sarek in the 2009 Star Trek reboot.
Shortly before his death he finished filming the horror feature The Devil’s Light for Lionsgate.
Cross has two children, Lauren and Theo.
