I joined the community to answer this because I feel your pain and very surprised to see the complete lack of viable assistance from sky themselves. My NowTV app was stuck on an old login of mine and would not let me sign out. Strangely on my older Apple TV devices I could sign out. Try the following:
Login to your old account via your phone, tablet, laptop.
Scroll down to authorised devices and delete them with the exception of the device you’re on.
On your Apple TV delete the app, restart the AppleTV, reinstall the app.
Open NowTV and scroll over to settings and you should be able to sign it.
This is what worked for me and I hope it works for you.
Given up trying to get this POS app to work. I refuse to reset my AppleTV just to get this useless crap working. Have emailed a complaint to Sky demanding a refund and won't subscribe again until they update this useless app.
@Tive @This did not work for me , not on my Apple TV 4 (HD) at least ... and I really don't want to reset my Apple TV .. that is long af . Not impressed with now tv. This is the exact same app they initially released about 6 years ago . That current update is a lie as far as I'm concerned or anyone in the Apple eco system! Not impressed @NowTvHelp