Also in UK & with BT.
I've just used the "change default DNS" solution (I used the google DNS: 8.8.8.8 & 8.8.4.4, but others available), mentioned elsewhere on the internet, it worked for me (on two devices). Now changed back to original settings (i.e. using ISP default DNS) and still working (on both). Didn't even need to reboot, just changed the settings, triggered an update successfully, then restored the settings.
Such a pity Microsoft haven't tried a little harder to keep users informed.
Just to confirm, the method I used did work exactly as described. DNS name resolution query result is being cached so when you revert back to the original setting it will continue to work, but only while the (working) DNS name resolution query result remains cached, once it has aged *(sorry, don't know how long that takes)*and is cleared from the cache, the issue returns. So you either need to keep with the non-default settings until the problem is eventually resolved (one assumes, but who knows when) or be prepared to switch between default DNS and overridden DNS settings when you want to force an update.
As updates on the eventual resolution of this problem are not very forthcoming (at least not without having to hunt around for them) it becomes a matter of deciding for yourself which is option works best for you or rather that you find least frustrating.