The Hunt for Tony Blair, which has been described as a spoof of 1950s film noir, imagines that the prime minister is wanted for murder.
Blair, who will be played by Mangan, is hoping to clear his name but after escaping from Number 10 he is forced to go on the run as no-one will hide him.
Saunders will star as Margaret Thatcher, while Robbie Coltrane and Inbetweeners star James Buckley will appear as the police officers hunting down Blair.
The cast also includes Nigel Planer as Mandelson, Ford Kiernan as Brown, Harry Enfield as Alistair Campbell, Catherine Shepherd as Blair's wife Cherie, Rik Mayall, Morgana Robinson, John Sessions and Ross Noble.
Channel 4's head of comedy Shane Allen described the one-hour film as "an irresistibly hilarious script from the godfathers of British comedy".
"Brilliantly conceived, we race through Blair's past as he's the wronged man (in his own head) on the run for mass murder," Allen continued. "So many juicy parts for the big comedy hitters of the Comic Strip team alongside some newer C4 comedy talents, it promises to be a very daring and utterly irreverent romp."
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