Manually setting the DNS settings won't effect anything if there is two DHCP servers on the network as they can cause IP address conflicts.
Also the OP has indicated they do have two BT smarthubs 😉
The OP has 2 hubs but they are not both connected.
As yet the OP has not confirmed that, or confirmed their network configuration. Doing both of these would help
Just one BT Smart Hub 2 connected
I received two others last week which were connected in turn but made no difference so original Smart Hub 2 is now connected
What other devices are you using on your network and also have you tried manually setting the network settings instead of using DCHP?
I would be extremely surprised if it is anything with your home network. I suspect it will be a problem in the BT infrastructure.
Quick update..
BT Openreach Engineer has just been and we might be getting somewhere as he has seen something similar in the past
He has spoken to someone in BT who thinks that following a system update, my broadband username does not match the one shown for the Smart Hub 2, namely the standard: bthomehub@btbroadband.com
Might have to wait up to 24hrs for a fix but hopefully they will escalate
Do you have a solid blue light on the smart hub?