I got a Nexus 7 from my wife yesterday for Chrimble and I have exactly the same problem.
Hence why I joined this forum.
I can connect to my BT Home Hub 3 OK with my iPod, our iPhones, our laptops, my desktop so the problem is not at the HH end.
When I start I see a list of available Wi-Fi access points including my HH as you do.
The access points that have something like BTWiFi or BTWiFi-with-FON in the name are the FON access points which do not have authentication. To use these you need the BT app which you can't download until you are up and running.
The access points that have BTHomeHub or BTHub in the name are the primary access points, looks like BThomehub2 is your own router. This is the one you need use by selecting it. You need to authenticate to use these - enter your WEP or WPA key (password) when prompted.
I assume you did this as mine also says "Authenticating..." when trying to connect.
Mine tries several times then gives up - grrrrrrr!!!
Sorry I don't have the solution yet but it's sort of good to know I am not alone.
I am on the BT help forum too - I will post there and see if anyone else has had the same problem.
I'll get back here if I find the answer.