My issue began via Amazon in UK. I started getting someone else's emails to my icloud e-address. A phone call with Amazon showed this person had changed their previous email registered with Amazon to mine and, according to Amazon, had successfully verified it! Concerning to say the least. As I write, Amazon are "reviewing" this and have said they'll get back to me in 48 hours. We'll see if they do.
I've contacted Apple by phone via the link provided by Roger Wimut1 above (thank you). While on the phone with Apple (I have to say I'm impressed by this level of instant support) I reset my Apple ID with a new password and verified that has worked. From this discussion with Apple support I'm fairly satisfied that my ID has not been compromised (yet!) which is important as I use it for many kinds of online stuff.
This seems to have come about from either subtle nefarious activity aimed at hacking my ID or a major security ****-up by Amazon. In either case, I hope I have stopped any further damage.
I hope my experience is useful to readers in similar circumstances.
If Amazon does get back to me, I'll post the result below.