You could always try disconnecting your hub from the phone line for a few minutes and then re-connecting. This will give you a different IP address and might also give you different DNS servers. There is not just one server, BT have multiple DNS servers and it is probably only one that is giving problems. It might not work as you might just pick up the same server again, but its worth a try.
Does anyone know of any number that we can call to get through to someone at BT in the UK who will listen to the issue, rather than insisting on spending over an hour plodding through their set list of 'fixes' that just don't work? Surely BT know that this is an issue?
BT will be aware of the issue, but how long they will take to fix it is another matter. Speaking to the call centre is a complete waste of time. In the short term (and in the long term if you wish) it is a simple matter to change the DNS servers that you use to the Google ones 188.8.131.52 and 184.108.40.206 Unfortunately the home hub is so nailed down that it is not possible to change DNS settings so you will have to change them individually on your devices.
Depends on your opinion of Google. I use Google DNS permanently. I also use the TP Link TD-W9980 modem/router which allows DNS servers to be set. I haven't got BT TV, but other posters have reported that it works fine with the latest firmware.
I don't believe the current problem can be widespread as there are very few posts of problems.