On the NOW TV boxes, when you go into the box Settings under Network, Set up Connection, Wireless.
It will show every Wireless Network available that can be detected and in the wifi range of the NOW TV box.
Each SSID network will have a padlock icon symbol next to it (including your own wifi network).
Normally on the NOW TV boxes, when you highlight your Network wifi name and press the OK button on the remote a new screen page appears on the television with a on screen keyboard to enter your new wifi password for the new BT Router.
Did this happen ?
Haven't used a BT Router in a number of years and not familiar with their newer Router models, but what i did on my old BT Hub 4 was to split the wifi Networks and try setting up the wifi on the NOW TV box on either 5ghz or 2.4ghz (where 2.4ghz worked best for me).
I also had issues with certain wifi devices that wouldn't play ball with my BT Hub 4 Router and had to disable the smart set up feature on the BT Hub Router itself.
Hopefully a factory reset on the NOW TV box which @gavs82008 mentioned will sort it out.