Hi Fred, welcome to the forum.
There really shouldn't be any problem using fixed local IP addresses, so long as your network interface is properly set up. The router should be acting as a DNS relay, and your network interface should specify the router LAN address as its default route. In the network interface you can give the router address as the DNS server, or you can specify the actual BT DNS server addresses. Either should work, but it might be worth trying the other option to what you have now.
Eric