The UK public are extremely conservative, and extremely misinformed by conservative news sources. That's at the root of a lot of the demand for authoritarianism.
But like I said, I’m not a political historian just an idiot with a half baked opinion.
All political movements and all politicians are convinced that their power is 100% legitimate and they should therefore be able to have 100% control of and visibility into everything that's going on.
The idea is compatible with most peoples' definition of democracy. You don't need to support other aspects of authoritarianism usually associated with right or left wing dictatorships.
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.
Also, I completely disagree that the world has mostly been moving away from authoritarianism. On the contrary. There was a time when at least the direction of travel seemed assured. Now I'm no longer so sure.
[Edit] Just so you know where I'm coming from. As someone who would never remotely associate himself with anything "conservative", I wish I could just blame conservatism or right wing authoritarians for this surveillance drive. But I can't honestly do that, and I have to accept that it is not just a right wing idea historically.
So please, debate policies on their content, not on their label. Reducing everything to a binary decision only serves authoritarian agendas.
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.
The Conservatives (aka Tories) are conservatives. The Labour party are also conservatives as much of the voting public in the uk is small-c conservative and also authoritarian.
While conservative news sources historically act in bad faith here, non-conservative news sources lose all reasoning ability, when it comes to Gov surveillance. They rarely hold Gov accountable unless they have little choice.
The latter probably happens because the public endlessly gives news orgs a pass about it.