Apple channel requires app to view show, what is this and what login would I use if downloaded the channels app

Because when I did that BritBox wouldn’t accept my icloud user id. So how would I login to the individual app. BritBox won’t tell me anything because they say I purchased the subscription under the Apple umbrella or thu Apple. Whichever they don’t like it and would prefer I pay them directly. But if I’m paying the same price Apple should ensure I have access to the same shows as I don’t see anything in the T&Cs that says I have a different subscription.

I apologize if the title of my question seems messed up. I think autocorrect or I did something screwy there. But the gist is that I cannot use my iCloud login that I use to subscribe under Apple TV to login to BritBox app or site. But beyond that I shouldn’t have to use a separate app to view their shows.

I appreciate your thorough answer. It seems almost as if BritBox is trying to punish people that signed up through the Apple TV app. It’s a new season of a show and they are dropping two episodes weekly but the latest two they dropped (the last one of this weeks two shows that dropped) literally has a small BritBox in the corner (sometimes) of the episodes’ picture and then of course when you click on it it says you must use the app to watch this show. It’s just odd as the new episodes that dropped last week and the week before are still available thru Apple TV just not the latest one. We aren’t having this issue with another show that is dropping new episodes weekly. I appreciate your help but think it may be time for Apple support. They should at least know about this and if this is the case I might as well just subscribe thru the app.