Fantastic! Thanks so much for this pointer; my problem is solved at last. I did try searching for threads on the same topic before posting this one, but clearly wasn't using the right terms.
The answer became clear in a post by Dark Laguna, though on re-reading the thread it was implied in things said by chaley and Isherwood, so kudos and thanks to all three of you. All I had to do was go to Preferences, Conversion, Output Options, Mobi Output, and then tick the box for "Use author sort for author". I re-sent the books, and hey presto! all is well.
Thanks to everyone for their patience and willingness to help.
Alison