This is a thorn in some people's sides. There have been times where people have simply not been able to find a solution, let's hope that's not the case here :P
I'm not with BT so I can't verify any local ISP issues, however, even if there were such issues it may be local to your area of the country. I would imagine a company like that would have some sort of phone number you can phone to check the service status of your connection, or phone them and ask to do some tests to make sure everything is fine. I'm sure it's not the whole of BT or we'd have hundreds of posts about it!
I assume you have a router (Re: signal strength comment) have you recently updated any firmware or got any updates through Microsoft Update that may have effected this? Also, have you tried totally disconnecting your modem/router, turning off the 'puter, then waiting 30 seconds and reconnecting it all? If you haven't checked for router updates then you may wish to and see if that helps.
Also, have you tried other networks than Gamesurge, is it happening on them all?
The hanging for a long period after connecting deffo sounds like an internet connection problem.