Saab Dastard's advice is good as always.
Here is another possible option.
You will be able to continue to leave your BT ROUTER attached to the network -
IF it is possible to disable its DHCP Server and assign a static address to it within your new network's address range.
Many ISP supplied routers are locked with respect to various configuration settings, the exact nature of the locked bits may well change with the router's software version too. To be certain you will probably need to check the specific device.
You might want to turn off the wireless too, or of course you can use it as a second access point if your premises are large.
This article purports to describe how to disable DHCP on a BT home Hub 3.
https://support.getcujo.com/support/...-bt-home-hub-3