You assume your premise. No the government actually doesn't 'have to' take action about mean things on the internet. The UK has such an obsession with regulating what is, essentially, politeness.
The UK, and I assume much of Europe, criminalizes truly petty levels of speech. For example, it's illegal to insult someone and cause them 'alarm' or 'distress' in the street.
Thus the non-technical populace see rudeness on the internet as the result of some kind of wild west situation that the government needs to control, to bring it in line with the rest of the public realm.