Entitled Walking The Dogs, the film will tell the tale of how Fagan gained entry to the palace and entered the Queen's bedroom in 1982.
Eddie Marsan and Russell Tovey will also star in the dramatisation.
The film, to be screened later this year, is part of a new drama series for Sky Arts called Playhouse Presents.
Brenda Blethyn, Stephen Fry, Richard E Grant and Sheila Hancock have also been lined up to star in new dramas that have been commissioned for the channel.
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