Sounds to me like it's an Apple issue. My PCs and Android devices (including tablets) work fine on the standard BT DNS settings.
But which ones? BT have many DNS servers and I suspect the problem lies with only one of them.
The problem is the way in which the DNS resolves some https which is why people are having problems with ipads downloading apps, newspaper updates etc.
Change the dns on the ipad to google and everything is fine. If you log on to a VPN and access sites though those then everything is fine. oday i tried to update apps using BT - my iphone would not complete the download. Switch off wifi and do the same on 3g/4g and there is not problem.
It is not a local issue or an apple issue, it's a BT DNS server issue and Ii wish they would just cough up to this so we can know what is going on. Saying that there is no problem when a significant number of people have the problem is not an answer IMHO.
Ironically all the standard web-based https stuff (BBC Facebook etc ) now works for me using the default DNS. As has been mentioned elswhere on here BT keeps refreshing the DNS server settings on hubs.
My hub updates at least once a day.
It has just done so.