New
#11
You can actually use third party routers. I don't think you're technically tied to them.
I think the answer may be due to the fact that the Bt Home hub 5 has gigabit 1000Mbps ethernet ports and the Talktalk hub has only 100Mbps ethernet ports, this will cause a significant drop in the speed of your internal network.
I guess for an internal network you could attach a gigabit switch to the hub and then run your network from the switch.
New ISP means resetting the power line adapters for the change. The Power line adapters have zero to do with the modem adjusting to the final stable speeds.
You would need to find the manufacturer instructions how to reset them. If you got a new router/gateway with your new ISP, you do not have to buy anything, because the new Gateway also contains the modem. Unplugging the modem/gateway is still not going to change anything.
If speeds are different with the new ISP when you connect directly to the new Modem/Gateway and are not showing peak speed through a speedtest. Get them back out to check things to see why the new modem is not showing peak speed available on its menu.