This. Governments are signatory to a huge number of agreements, and are members of various NGOs. Things start out as being representative of some will of the people, but over time it becomes a millstone around the government's neck if it the arrangement becomes politically difficult at home. And of course, those arrangements often morph to be to the benefit of those in charge.
What happens is that you get arrangements like the EU demanding migration quotas that the populations of various individual countries despise, or an automobile market that gets progressively more expensive as environmental legislation puts ever more pressure on manufacturers. And of course, if you're saving the world, who needs cars anyway? We should all be living Hong Kong style to save the environment, so we need more urban density.
I think what’s happening isn’t some evil plot to quell opposing voices, but more likely the UK government thinking they’re actually passing laws to reduce rioting and online abuse. And the censorship effects are a side effect of these laws.
Some might consider this opinion naive but take this counterpoint: laws require a majority to pass. So if these censorship laws were written to squash opposing voices, then we’d be dealing with a literal conspiracy involving hundreds of people. I don’t believe all politicians are only in it for themselves (though I do believe many are), so you’d expect at least 1 MP to speak out if such a conspiracy existed.