There have been some instances of people being inappropriately contacted by the police over things they wrote online. I think that this has largely stopped following the court judgment that I mention downthread. I think there's broad agreement here on what the police should and shouldn't be doing. The issue is whether it's actually accurate to paint a picture of the UK as a country where the police regularly harass people about their online postings. If people in the UK strike you as unduly unconcerned, consider the possibility that it's because this isn't actually happening to anything like the extent that some people on Twitter would like you to believe that it does.
By the way, you seem to be using 'the government' in a very broad 90s internet libertarian sense. The police in the UK are operationally independent of the government of the day. As Wikipedia explains:
> Police officers [in the UK] hold office and are not employees. Each officer is an independent legal official and not an "agent of the police force, police authority or government". This allows the police their unique status and notionally provides the citizens of the UK a protection from any government that might wish unlawfully to use the police as an instrument against them.