Well, the problem with my payment method, anyway. The nice chap who rang me in answer to my ...detailed... email, still couldn't work out the free one, but did enter into the spirit of things by finding it very amusing......
However, apparently when my card was renewed (by Amazon) they do not update the details of your (Amazon) card, which therefore means the (Amazon) card they (Amazon) try to take payment (to Amazon) from... is invalid.
So I (me) had to go online into my account and, basically, tell Amazon they have delivered, authorised and registered my new card for use, (which obviously they know) and that they should take monies from that card - instead of the one they can't take monies from because it's invalid.
I suppose it's security or something , but I definitely didn't think of it.
This may be the paperless society, but it often doesn't seem to be any less complicated....