Getting a remote desktop client to work can be a pain. Having used OS X's default share screen option on a local network and found it good, but lacking in some respects, I typically wanted more control. Apple Remote Desktop seemed the logical extension to that.
Getting it to work in anyway with the BT Homehub 3 was far from clear, but after many attempts at trying everything possible, and asking the IT guy at work, it's now working. For my own sanity and those in the same situation it's only good to share, so here is my solution.