...And during all that time, the BT DNS service was not working, so I couldn't do any other work. #RANT# The BT-supplied router, the fornicating clunky useless and slow Home Hub 5, does not allow you to put in your own DNS servers...
1. Never rely on routers supplied by ISPs (especially BT), they reliably suck giant fucking donkey balls.
2. Your OS doesn't have to (and arguably shouldn't) use the DNS server address given by the DHCP (router).
Arguably you should specify the DNS on your OS for security purposes anyway (e.g a compromised router sending all your DNS requests to a malicious server and sending you off to some amazon.com impersonation... that's what you risk every time your computer connects to a public AP).
Another reason not to use ISP's DNS is they all poison it these days, I'm not on BT anymore but they used to redirect all missing DNS entries to their search page with loads of advertising... I can't begin to go into whats wrong with that because i'd take too long.