Well I finally found a way to send mail to local recipients, quite by chance really.
I have a POP3 mailbox set up at Gradwell.net to allow me to send mail to 'myself' on my home machine (I read just about all of my mail on a remote machine at Gradwell) which comes in useful occasionally when I want to send a file to my home Linux box. This is set up in my isbd.net on Gradwell so it's home@isbd.net. I just occasionally run mutt locally on my desktop machine and collect mail from this POP3 mailbox.
So, I realised that one way around my problem of sending mail to myself on the desktop machine would be to put home@isbd.net as the alias for root mail in /etc/aliases. Before doing this I tried sending mail to home@isbd.net from my desktop machine, it failed with "Error sending message, child exited 67 (User unknown.).", huh? I then realised that this meant that sendmail was trying to send this *locally* and there's no user called 'home' on this machine.
Euraka!!! If I send mail to chris@isbd.net on my desktop machine it gets sent to the local user chris and *not* to the place where it would get sent if it was sent from anywhere else on the internet (chris@isbd.net is one of my 'real' E-Mail addresses).
So, problem solved, I can put:-
root: chris@isbd.net
at the end of /etc/aliases and all the root mail will get to me locally.
Quite *why* it's like this is anybody's guess! :-)