I managed to install OpenWRT to my new router and switched to it completely. Thanks everyone for help!
Let me sum up and mark this post as a solution.
In order to connect a custom third-party router to BT (British Telecom) when using Optical Network Terminal (ONT) do the following:
Configure the router to connect with PPPoE
The username should be of the format bthomehub@btbroadband.com. No password is required, but if the router insists, use bt as the password
If router cannot bring WAN interface up try removing the default VLAN records.
Addtional info