I've got an HTC One M8 that connects perfectly happily to every network I've tried except for one - and I get exactly the same message on another Android device as well - one is running Lollipop and the other KitKat. Whether it's the network (Virgin, as it happens) or the hardware, I'm not sure (fortunately it's not one I want to use often). I think your best bet would be to talk to BT as I think hardware interfacing is the most likely issue. They may be able to suggest something you can do in the router settings. I couldn't see anything in the settings on the phone that would have any effect.
Googling the issue suggests a couple of things:
Too many devices trying to connect.
Channel interference from other routers, which a channel change would fix.
Both those can be changed, afaik, but I don't know the exact procedure on your router. One for BT, definitely.
