This has been an intermittant issue for ages. I get around it by using google dns but as mentioned previously the servers are not as fast as BT!
Today this issue is hitting common web sites for me: BBC, Facebook etc even BT! Anything with https. I had a web chat on mybt with a nice chap called Santosh who was very helpful but had never heard of this issue and seemed to know little about the concept of DNS. He suggested that I call the helpline. I sent him the link to this page.
The last time this happened in our area for any length of time was two weeks ago. Microsoft and others were hit with a huge DDOS attack.
It strikes me either BT are in denial or coping with some issues that they don't want to share with us.
Problems with exactly the same webpages. Had a similar talk on the live chat as well. Said the problem will be monitored and I can expect a callback on Saturday. Losing a bit of faith, though, as none of the other checks/etc. have made any difference.
As a temporary measure, just change your DNS to 18.104.22.168 and 22.214.171.124. You can't change it on a Home HUb if you have one, but you can change it on your PC/device
If you can setup your own DHCP server, instead of using the home hub, you can set the DNS servers for your whole network.
I have the DHCP server on my home hub turned off, and instead use my wireless access point which has its own DHCP server which is configured to use OpenDNS.
That way you do not have to alter any devices, as the DHCP server provides both LAN and wireless requests.
I use a TP-LINK TL-WA701ND access point, but you could probably use an old unused router to do the same thing.
This issue is now resolved. http://status.aws.amazon.com/ under Amazon CloudFront gives the details. It was causing problems, apparently, from 1107 until 1741 (UK time). There was a conflict with BT's DNS. Amazon Prime Music stopped working and other sites using Amazon's cloud service where interrupted.