Does the bt hub let you turn off DHCP? I had a similar issue with my ISP router, but it let me turn off dhcp and then I ran pihole which can run its own DHCP server.

Then, the DHCP server can tell all clients to use your preferred DNS server.

I haven't used adguard, but it can probably do the same. If not, you can run a DHCP client on the same box probably.