The four-part series, based on the novel A Very British Coup, focuses on the aftermath of an industrial accident in Teeside which raises questions about the US petrochemical company involved.
In Treatment star Gabriel Byrne has already joined the cast as a politician determined to maintain his integrity and uncover the truth.
However, he struggles to keep his party on side, faces revelations about his personal life and starts to realise that the government has links to the petrochemical company.
Channel 4 has now announced that Dance and Graves have both landed parts in the series alongside Robin Hood's Douglas Hodge, The Last Detective's Lia Williams, Misfits star Ruth Negga, Case Histories's Sylvestra Le Touzel and Gina McKee.
The drama has been written by Lennon Naked scribe Robert Jones and filming has already started in Manchester, Liverpool and London.
Coup is due to air on Channel 4 later this year.
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