Anyone know how to restart BritBox on MacBook Pro Apple TV?

If you subscribed to the BritBox channel inside the Apple TV app, then that would be available on macOS Catalina 10.15 or later with the TV app, as well as other devices with the Apple TV app.

Subscribe to Apple TV channels in the Apple TV app - Apple Support

If you subscribed to BritBox outside the Apple TV app, then you would get access to BritBox through the separate BritBox app (on iPhone, iPad, or Apple TV box). That is a different type of subscription, with different terms and conditions, different perks and limitations, and not exchangeable as such. If subscribed with BritBox directly, then you would have web access as well.

See your subscriptions overview - Apple. Verify that BritBox is listed as an active subscription. Check how it is listed. Does it say “tv channels” after the channel name?

Meanwhile, I cancelled BritBox via Apple and will wait a month and then try re-subscribing to see it that works.

You are free to do so, of course, but that may not have been necessary. If it happens again in the future, then please contact the Apple Media Services staff for further assistance. They may be able to check your account properties and subscriptions, as well as the BritBox content server-side.