The Alfie star plays actress Tippi Hedren opposite Toby Jones as legendary director Hitchcock in the film, which tells the story of the pair's tumultuous relationship during the making of 1963's The Birds.
Miller's portrayal has earned her a Leading Actress nod, while Jones is included in the Leading Actor category. The film also scooped a mention for Imelda Staunton (Supporting Actress), as well as a nomination for the Single Drama prize.
U.K. Tv series Parade's End is also among the top nominees, scoring seven nods, including a Lead Actress nomination for its star Rebecca Hall. She will compete against Miller for the title, along with Anne Reid (Last Tango in Halifax) and Sheridan Smith (Mrs Biggs).
In the Leading Actor category, Jones will go up against Skyfall star Ben Whishaw for Richard Ii (The Hollow Crown), as well as Derek Jacobi (Last Tango in Halifax) and Sean Bean (Accused).
Bean's show Accused scooped a further five nominations.
In the International category, popular drama Homeland will go up against Girls, Game of Thrones and The Bridge.
The British Academy of Film and Television Arts (Bafta) Tv Awards will be handed out in London on 12 May (13).