It is possible to have remote access to most routers as you will see if you log into the router management. Usually the option is not available by default but I have never checked this with a BT HomeHub. Whether controlling a router remotely can be seen by the computer linked to it I'm not sure either.
It may be that BT do have remote access option for their routers. If they have your IP address, which they will have, in theory it is possible in the same way that you can log into any other computer that is on the internet. Providing you have the log in credentials.