Basically you need to determine whether you've got a broadband issue, a powerline adapter issue, a network hub issue. Its NOT likely to be anything to do with the BT Ultra box if you're continuing to have problems on the PS4. From the way you've said things below it sounds like you've changed to BT broadband at the same time as getting BT TV?
If you plug the PS4 directly into the powerline adapter i.e. not the powered switch. Do you still get dire speeds? Can you plug a laptop into the powerline adapter and do a speed test to see what you actually get over this adapter? if the speed is dire then it points to a powerline adapter issue (assuming the test below is okay). If the speed from the powerline adapter is okay that point to a network switch issue (order one on Amazon to try and then return if all okay?)
If you are still getting issues with something directly plugged into the Powerline adapter then you need to plug something directly into the Home Hub and test that (take the lead from the powerline adapater that the hub is plugged into and use that). I am assuming that generally you are getting WiFi in the home okay? if so then that suggests the broadband coming in is fine.
You may just be unlucky that your network switch and/or powerline adapter have got a fault.
I would say that the issue is with the powerline adapters, they cannot cope with the extra speed needed, and all the multicast data as well, which is needed for the YouView box.
The multicast streams are overloading them, which is why the PS4 is slow as well.
It may be better to try totally different adapters.