Every English gun case I have has covers on some of the compartments, albeit some more than others.
I think you're cases are the exception to the rule, Kid. Regardless of age, the many, many cases I've seen, rarely have covered compartments, and except for some terribly high-end Purdey and H&H guns, I've never seen a covered case that's come straight from the maker. As others have mentioned, it's more a 'french thing', than English.
Either way, I like it, and I'm thinking of heading down the path of putting a scene on the cover, like Mr. Larson. Now, I don't have the artistic ability to draw a stick man, but I'm already thinking maybe some Sporting Classic covers or something would work.