Update: I have recently taken annoyance to some of the details on this post, so removed them. I guess you will never know.
Well, it has to be said that BT Infinity fibre broadband is pretty awesome. It also has to be said the BT Home Hub is pretty woeful. It is actually pretty irritating, the a service so good can be controlled by something so bad. Anyone with any self-respect will want to swap it out, and here is how.
First, you need to keep the NTE. That is the white box. You are going to connect this to the ethernet interface of your Cisco router - assuming it supports vdsl - and give it these commands:
interface FastEthernet0/0 - or whatever will be your WAN interface
no ip address
pppoe enable group global
pppoe-client dial-pool-number 1
ip address negotiated
no ip unreachables
ip nat outside
dialer pool 1
no cdp enable
ppp authentication chap pap callin
ppp chap hostname email@example.com
ppp chap password 7 0117090D5704090435444F1D0A1102020208
ppp pap sent-username firstname.lastname@example.org password 7 0117090D5704090435444F1D0A1102020208
ppp ipcp dns request
ip route 0.0.0.0 0.0.0.0 Dialer1
You will of course need to NAT. Now, like me, I didn't have a wireless router, but don't worry. Plug a LAN port of the Home Hub into your Cisco network and simple disable DHCP on the Homehub. The DHCP on your Cisco will give out the correct gateway and the Home Hub switch the wireless traffic.
Done. Good work.