She has already won a Golden Globe for Steve Jobs, in which she played the Apple guru's right-hand woman.
Tom Courtenay and Charlotte Rampling, stars of marital drama 45 Years, were named best actor and best actress.
The British film won three awards, equalling the tally of Mad Max: Fury Road at the central London ceremony.
Post-apocalyptic thriller Mad Max: Fury Road was named film of the year by the UK's film critics, while George Miller received the director of the year award.
Tom Hardy was named British/Irish actor of the year for his 2015 body of work, including Mad Max, Oscar frontrunner The Revenant and Legend, in which he played the Kray twins.
Sir Kenneth Branagh arrived at the event with Dame Judi Dench, who presented him with the Dilys Powell Award for excellence in film. The pair have recently appeared together on stage in A Winter's Tale.
The British/Irish actress of the year prize went to Saoirse Ronan for Colm Toibin's Brooklyn.
Despite scoring seven nominations, Cate Blanchett romance Carol only won one award, for cinematography.
Winslet, speaking of the nomination that could see her win a second Oscar, said: "I really can't believe it because it has been a very strong year.
"No one has been a shoo-in. People have been flitting in and out of this best supporting actress category for quite some time.
"They were like the golden tickets this year. They were really very coveted spots, particularly in this category, so I'm absolutely thrilled. I loved the experience of making it so it's ultimate cherry on the cake to be nominated."
She tipped Leonardo DiCaprio for the best actor Oscar for The Revenant, saying that it is "probably going to be Leo's year".
"I think you can sort of feel it and I think everyone wants it for him," added Winslet, who won the best actress Oscar for 2008 film The Reader.
45 Years, based on a short story by David Constantine, shows the lives of married couple Kate and Geoff whose relationship is threatened as they prepare for their 45th wedding anniversary.
It has also been nominated for best British film at next month's Bafta film awards.
Rampling is in the running for the best actress award at next month's Academy Awards for her role in 45 Years, which was named the British/Irish film of the year.
Fellow Oscar contender Mark Rylance was named best supporting actor at the awards, at London's May Fair hotel, for Bridge of Spies.
Other winners included Asif Kapadia's Amy Winehouse film, Amy, which was named documentary of the year, and Game of Thrones actress Maisie Williams, who won the young British/Irish performer award for her role in The Falling.
Benjamin Cleary, also in the running for the Academy Awards, won the British/Irish short film of the year award for Stutterer.
Kate Winslet has been named best supporting actress at the London Critics' Circle Film Awards, days after receiving an Oscar nomination.