Set to begin shooting in London and the South of France in August, the limited series is expected to air on Sky Atlantic in the United Kingdom and Showtime in the United States.
Leigh and Weaving will play the parents of Cumberbatch's title character, while Anna Madeley will play Melrose's wife.
David Nicholls is writing all five episodes of the television adaptation of Edward St. Aubyn's novels and Edward Berger is directing.
Showtime described the series in a press release as a story that "hilariously skewers the upper class as it tracks the protagonist's harrowing odyssey from a deeply traumatic childhood through adult substance abuse and, ultimately, toward recovery."
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