1) install the Now TV app on your smartphone. You've now got subtitles on the phone's little screen, but you want it on the big screen, so..
2) go onto Ebay and get a Chromecast device (I got a 3rd gen unit for £22, 2nd hand. Good enough for me, but if you want 4K UHD then you'll need the latest version). Its about the size of a computer mouse.
3) attach the Chromecast to a spare HDMI port on your TV. If (like me) you haven't got a spare port, then you can just disconnect the cable from the BT TV set-top box as you can't watch 2 things at once. If you dont want to mess about with cables, then get a HDMI Switch (not a splitter) that lets you manually switch between video sources.
4) setup the Chromecast by running the Google Home app on your smartphone (do a factory reset on the C/C first if its 2nd hand). This takes 5 minutes.
5) go back to the Now TV app on your smartphone, play the video and press the 'Cast' icon at the top of the screen.
That's it - you should now see NOW TV with subtitles playing on the big screen. A bit of a palaver, but ok as a work-around until the developers get round to fixing things on the BT settop box.
Re: Now TV - how to get subtitles on the TV screen
Here's another way :
If you have a 'Smart' TV (i.e the TV itself is internet-connected and has apps built-in , which you have probably never used, since their functionality is duplicated on the BT TV settop box) then see if the TV has a NOW app installed. If it hasn't you can probably get the TV to download it (e.g. Samsung TV's have a selectable library of apps). The app will probably support subtitles with no further ado. You will have to sign into NOW with the account you possess by virtue of your BT TV subscription.