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.

Do you think if I say "hello", and this is my first communication to you, and you feel threatened, and we're in the UK, I will be arrested?

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).

So do you think an offence was committed in this scenario?

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.