Try something like DNSBench to test alternative servers. I use a mix from different DNS providers in case any one has issues. Remember some (such as openDNS) divert some web requests; there are good and bad reasons for this but you should decide if that is what you want.
As Jonkarra said: Don't forget if you have any level of BT nanny control on it will probably stop any non-BT DNS servers working.
Where do I check to see if I have parental control..
Actually, I haven't even set BT parental on so I doubt I have it on
Login to your account on bt.com on the page after you've logged in scroll down to BT parental controls its at the bottom second from left option. If it says Activate then it should be disabled but might be worth activating and then disabling it to be sure.