I appreciate you taking a look ... I suspect I have messed up the access controls ... I found them quite confusing and haven't really got my head around what the 'therapists' will need.
Just so that you know I am the only administrator and I don't allow anyone else access to the website ... so other than 'therapists' and 'guests' no one else does anything on the website.
Checking the Access settings for the Therapist in London post type I see that therapists don't have publish rights. They can't be set as authors if they don't have the right to publish.
I've changed that, and now the author dropdown contains all of the therapist users.
Thanks again for your help. Although I still need to work on how the 'therapists' will edit their own page, without getting access to the back end and options that might confuse them or that I don't want them to see, I think I'll say that this issues is resolved.
I am going to probably open another ticket, but only once I have checked to see if there is any documentation on how to resolve the next things.