If you subscribed to BritBox through your Amazon Prime Video Channels account, you won't be able to use that subscription to sign in at BritBox.com or on the BritBox mobile, tablet, or TV apps.
You'll only be able to watch BritBox on the platform where you signed up.
For additional context:
Since you subscribed to BritBox through Amazon Prime Video Channels, you won't be able to log in at BritBox.com using your Amazon Prime Video account. Instead, you’ll need to watch BritBox through the Amazon Prime Video app.