Film Stars Don’t Die In Liverpool, which also reunites Billy Elliot favourites Jamie Bell and Julie Walters, is due out in November.
Watch the full trailer above.
Set in 1978, the film picks up with the vibrant affair between Oscar winner Grahame and the young Peter Turner (Bell).
He becomes the person she turns to for comfort, only for events beyond their control to truly test their lust for life.
Paul McGuigan has directed the drama, which is based on the memoir of the same name by Turner.
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Vanessa Redgrave, Kenneth Cranham and Stephen Graham also star.
Early reviews have been positive, with The Guardian awarding four stars.
Variety and The Hollywood Reporter have also returned enthusiastic verdicts following the Telluride Film Festival.
The film’s European premiere will be at the BFI London Film Festival at the May Fair Hotel Gala on Wednesday 11 October.
It hits cinemas on November 17.