But the Labour party have never been especially liberal. They're just as likely to enact controlling social policy. And, again, the press are extremely illiberal, they're likely to campaign for more surveillance.
(Don't try to jam the American two-party lens onto UK four-plus party politics, it will not help you make sense of the actual situation).
Because the UK has FPTP elections, in practice it's a two party system but which two parties varies by locale, resulting in some weird interactions that aren't really seen in the US.
You aren't going to get elaborate rainbow coalitions under that model, as you might in say Germany.
Labour are the party who passed that very nasty "Tell us your password or go to prison" law under "If you've done nothing wrong, you've got nothing to hide from law enforcement or the government." mentality.
Red Tories are still Tories.
This leaves the Lib Dems, who sadly have zero interest in repealing the Online Safety Bill if it passes.
But like I said, I’m not a political historian just an idiot with a half baked opinion.
As to your question: yes, most authoritarians are conservative in nature, given that the world has mostly been moving away from authoritarianism over the past few decades.