The awards will be presented Feb. 8 at London's Royal Opera House.
Along with Fiennes, Leading Actor nominees include Benedict Cumberbatch ("Sherlock," Frankenstein) for "The Imitation Game," Tony Award winner Eddie Redmayne (Red, "Les Miserables") for "The Theory Of Everything," Jake Gyllenhaal (Constellations, If There Is I Haven't Found It Yet) for "Nightcrawler" and Michael Keaton ("Batman," "30 Rock") for "Birdman."
"Birdman" received a total of 10 nominations, including Best Film, Best Supporting Actress, which went to Emma Stone (Cabaret, "Spider-Man"), and Supporting Actor, which went to Edward Norton ("Primal Fear," "Everyone Says I Love You"). Tony nominee Ethan Hawke (The Coast of Utopia, Macbeth) was also nominated for Supporting Actor for "Boyhood."
Leading Actress nominees also include Amy Adams for "Big Eyes," Julianne Moore for "Still Alice," Felicity Jones for "The Theory of Everything," Reese Witherspoon for "Wild" and Rosamund Pike for "Gone Girl." Rob Marshall's film adaptation of the Stephen Sondheim-James Lapine musical Into the Woods was recognized for Costume Design by Colleen Atwood and Make Up and Hair by Peter Swords King and J. Roy Helland.
"Pride," the story of a collaboration between British gay rights activists and miners, helmed by Matilda The Musical director Matthew Warchus, was nominated for Outstanding British Film, and Imelda Staunton received a nomination for Supporting Actress for her role in the film.
Visit awards.bafta.org for a complete list of nominees and more information.