Have you been using the apps previously? If so does the log in box appear when you run the app?
On yout iPhone, log out from the app from the 3 bars at the top lh corner, close all apps and re-boot the phone. Start the app and then try logging in via the 3 bar link at the top lh corner again.
With the TV try making sure that you close the app fully, then restart it (the same logging out/in process may work).
Presumably you have the Extra subscription that allows up to 4 devices?
Have you checked that your devices are still registered? It's two devices with the basic BT TV app and 4 devices with BT TV App extra, and I'm sure that you can only use the smart TV app if you have the Extra subscription.