In reply to:
The main difference seems to be that his Demon account uses a static IP address whereas mine is dynamic. I selected fixed IP and entered the specified address in the PPPoA set up menu but the router seems to ignore it - after applying the settings the router consistently listed the IP address as N/A.
Demon always used to require you to leave the IP to be set automatically by the ISP. Even if they don't require that, it should always work, even with a fixed IP.
I doubt whether you really connected to Demon using the Orange connection, if the router had a Demon login and password correctly set, then you will have used the ADSL connection in your house to connect to Demon, not Orange. That verifies that the router is correctly configured for the Demon connection. Take it back to the other site without changing anything and see if still doesn't work - if it doesn't it gives strong support for the line having a problem.
If, however, you merely configured the router to connect to your Orange account, then you have proved very little, it may simply be the login and password that are incorrect for the Demon account. Can you connect to the BT Test login?
http://www.adslguide.org.uk/qanda.asp?faq=troubleshooting#Q132
If you can, there is nothing wrong with your line or connection to it, and the problem is in the connection to Demon across it - login and password would be the favourites there.