My TV says it came run 4K/UHD just fine on 35mbps - I have the full 80.
I had 1 problem with my line in that congestion hit, but after I dealt with some guys in Newcastle I was moved onto a less congested segment (their words) and it ran all the time until I moved over to another Provider.
But it does sound like you are on the 40/10 product, which I think should now be 52mbps minimum? I think BT put the speed of the Infinity 1 to that to give people a bit more if they can get it.
As for BT TV, take it from someone who had it - it's pants. an IPTV service from Ebay would give you better HD and on demand contact - again I had it - and I still do.
Edit: Most TV's come with the Smart IPTV app - and if not you can download it.
Edited by 23Prince (Tue 25-Oct-16 11:13:15)