Well, no, more accurately, when it comes to it, it's in the eyes of a judge (or a jury in some cases). You can have all kinds of arguments about validity of arrests, of prosecutions, etc., but it's still fundamentally a system where you'll be charged with an offence and then either convicted or not.
I don't know of a single case (and don't believe anyone can point to one) where people have been arrested for simply criticising politicians. Has the number of incidents risen over recent years? Yes, and while this might be partly explained by stricter legal approaches, I suspect it's much more to do with a drastic rise in far-right activity and a consequent feeling among many that they can now say/do whatever they like with impunity (including making threatening and inflammatory remarks about minorities, and so on).
Not exactly a judge or jury. IIRC a common law assault can go on with only the subjective experience of threat. Hard to prove, but the bar is not objective. See:
True, although even those crimes (take common law assault) will still be heard in front of a magistrate - there's a process, there are processes for appealing, and it's not just some random police officer with the ability to jail you without process.
I agree that the UK has far too many laws that are more subjective than they ideally should be, but they do at least attach some level of observable and knowable process.
That would require the police to believe that an offence is likely to have been committed. While I am more than ready to criticise the police for many, many things, I'm not sure they're likely to just take that at face value... (As you've specified first contact, etc., that seems likely - of course there could be situations where such a communication would be an offence, such as in the context of a restraining/exclusion order, etc., but not in this case).
In the scenario which you've outlined, where you say "hello" to me, having never spoken to me before? No, I don't think that's an offence, but more to the point, whether I did or not, the police are unlikely to. We don't operate in a system where the police simply take the word of anyone who reports a feeling, the police have a duty to assess whether a crime has likely occurred.
I don't know of a single case (and don't believe anyone can point to one) where people have been arrested for simply criticising politicians. Has the number of incidents risen over recent years? Yes, and while this might be partly explained by stricter legal approaches, I suspect it's much more to do with a drastic rise in far-right activity and a consequent feeling among many that they can now say/do whatever they like with impunity (including making threatening and inflammatory remarks about minorities, and so on).