Cate Blanchett and Rooney Mara are both up for actress of the year, while Todd Haynes' film is also one of 10 titles up for the film of the year award.
Tom Hardy has three nominations that recognise his roles in The Revenant, Legend and his whole body of 2015 work.
Sir Kenneth Branagh will get a special award at the ceremony on 17 January.
Carol, which tells of a shopgirl who falls in love with a wealthy socialite in 1950s New York, gets additional nominations for its direction, screenplay, score and cinematography.
Marital drama 45 Years comes close behind with six nominations, two of them - actress of the year and British actress of the year - for its  star Charlotte Rampling.
Mad Max: Fury Road, The Revenant and Steve Jobs have five nominations apiece, while Brooklyn, Ex Machina and Room have four.
Amy Winehouse documentary Amy, meanwhile, achieves a notable hat-trick by being nominated for best film, best British film and best documentary.
Other titles up for the film of the year award include Disney/Pixar animation Inside Out, Ridley Scott's The Martian and hard-hitting documentary The Look of Silence.
More than 200 titles were put forward for the film of the year award by the Critics' Circle Film Section, whose membership is made up of more than 145 broadcasters, critics and writers.
"There was love for everything from Tangerine and Tangerines to Love, Joy and The Hateful Eight," said Rich Cline, chair of the Critics' Circle Film Awards.
"Getting to that final list of nominees certainly wasn't easy this year."
Last year's awards saw Boyhood named film of the year, with additional prizes going to its director Richard Linklater and cast member Patricia Arquette.
Sightseers stars Alice Lowe and Steve Oram will return to co-host the 2016 ceremony at London's May Fair Hotel.
Romantic drama Carol leads the field at the London Critics' Circle Film Awards, having received seven nominations from the UK's film reviewers.