The drama, which has been comissioned by Sky Arts, is about a real-life break-in that occured in the Queen's bedroom at Buckingham Palace in 1982.
In the original incident, 31-year-old Michael Fagan broke into the Queen's bedroom in the middle of the night. The two then had a long conversation before the Queen summoned guards.
Fagan, who claimed he had been having a breakdown in the wake of a recent split from his wife, was charged with theft of wine, though the charge was later dropped. He will be played by Eddie Marsen in the film.
Russell Tovey will play a footman who becomes entangled in the drama.
Now 61 years old, Fagan told The Daily Telegraph: "It was just a moment of madness. For her to be dragged through the dirt by me isn't nice. And how can they make a drama? They don't know what happened in there."
Walking the Dogs is scheduled to air later this year.
Emma Thompson will next be seen in Effie alongside Dakota Fanning.
She will also play Queen Elinor in the much-anticipated Pixar movie Brave.
Watch the brand new trailer for Brave below: