when I sign in to my apple id, I get a notification but it shows a wrong location.

I have the same Middlesborough / BT Broadband combination

Yes. I am using BT broadband. Does that explain it?

yes

Exact same problem. Went to the trouble of changing all passwords and now it seems it is just an Apple problem...

My pleasure.

I just gave up on this new system, I'm afraid. Until they can sort out all the annoying 'you're being hacked' messages and endless passcode requests, I'll be content with what we had before.

I would be curious to see a screenshot of the "you're being hacked" message you're referring to.