Hi TheDalek,
Thank you for using the Apple Support Communities.
We understand that the Apple TV app on your Smart TV will sometimes show a "no internet connection" message and we are happy to help.
"If you have trouble streaming, watching, or starting a movie or TV show that you purchased over a Wi-Fi or cellular connection," follow these steps: If you can't watch or stream movies and TV shows in the Apple TV app
If the issue persists, Reset the Apple TV app.
To find more answers to questions about the Apple TV app, visit the TV Support website.
Best regards.