Redmayne and Day-Lewis are nominated for their turns in Les Misérables and Lincoln respectively, competing with Toby Jones for Berberian Sound Studio.
Skyfall is in competition for 'Film of the Year', competing against Berberian Sound Studio and Ben Wheatley's Sightseers.
Sightseers co-writer and star Alice Lowe is nominated for 'Best Actress', alongside Andrea Riseborough (Shadow Dancer) and Charlotte Rampling (I, Anna).
Watch Alice Lowe and Steve Oram discuss Sightseers with Digital Spy below:
Chris O'Dowd (The Sapphires), Martin McDonagh (Seven Psychopaths) and Wheatley will compete for the Peter Sellers Award for Comedy.
Michael Fassbender and Olivia Colman took the top acting prizes at last year's ceremony for their performances in Shame and Tyrannosaur respectively.
The London Evening Standard British Film Awards are judged by a panel of film critics, and the winners will be announced in a ceremony in London on February 4.
> 'Berberian Sound Studio' director Peter Strickland interview
> 'Skyfall' Oscars snub is a pity, says Judi Dench
Watch Toby Jones discuss Berberian Sound Studio with Digital Spy below: