OK Kovid, with heart in mouth, I deleted all of the books in the Mantano library. I then used Calibre to send all books in the Calibre library to the Nexus 7. I then told Mantano to import all of the books into its library after I had found them in the directory where they had been placed by Calibre.
I then told Calibre on the PC to delete one of those books, and I checked in the correct directory and it had gone. However, it is still in Mantano Reader, so I suspect that you are right about Calibre not being able to mess with the Mantano 'private library'.
However, all is working well, despite the fact that it now seems that I have double copies of all my books - one set in the download directory and the other in Mantano! Oh well, I will worry about that if I start to run out of space...
Thanks again. John