There does not seem to be any option play my physical cds on my laptop disk drive using Amazon Music Player. Is that correct?
There is nothing on this in Help.
I contacted "Chat" and they say it is not possible.
I find this very stange. (I can play my own cds from iPlayer for instance.)
That is true but there are loads of other players why not download one of those or if you have iPlayer just use that. I don't know which operating system you have on your laptop but I just put a CD into the CD drive and it plays.
Or upload your CDs to the Amazon cloud and use Amazon's player.