If you can change the pre-set DNS setting sin the router that get assigned to your lan, set them to 8.8.8.8 and 8.8.4.4 which are google's DNS server. You probably cant do that on the home-hub though, i hate those terrible routers.
You could try another router if you have one, or see if setting the DNS servers on the client fixes it, i.e. on your pc set your TCP/IP setting DNS servers to the above, rather than auto-assign: 4 Images below.
If that fixes the issue on that 1 client you set it for, then you can safely assume it's a DNS issue and BT's predefined DNS servers are either unable or unwilling to handle the request. Also, to confirm DNS, you can try this:
if you ping google.co.uk and get the IP for it, i.e. for me it's 216.58.206.78, going to
http://216.58.206.78 will take you to the google page, as it wont require a DNS lookup to convert the google.com name into an address. If that still doesnt work, then presumably BT are dropping your request to google which is more problematic.