It's not really a problem in practice. The UK follows EU food labeling rules, at least for now, and so this is a real (not hypothetical) situation.
The easy way is to make it clear through trade dress. Parmesan is normally sold in wedge-shaped plastic trays, in the cheese aisle. So are other grano-type cheeses like Grano Padana. So essentially everything in that packaging is 'parmesan-like'. For the crappy pre-grated stuff in tubs it'll have a label like 'Italian-style hard cheese'.
Same is true of Champagne. The other sparkling wines also come in sparkling wine bottles. And are labeled Cava, Prosecco, Three Choirs Special Reserve, or whatever.
Personally, I much prefer actual parmesan to other (even very similar) Italian cheeses, but am not a fan of most champagnes. So I'd say that the PDO-style accurate labeling was a net positive to me as a consumer, leaving aside the economic protectionism bit.
The easy way is to make it clear through trade dress. Parmesan is normally sold in wedge-shaped plastic trays, in the cheese aisle. So are other grano-type cheeses like Grano Padana. So essentially everything in that packaging is 'parmesan-like'. For the crappy pre-grated stuff in tubs it'll have a label like 'Italian-style hard cheese'.
Same is true of Champagne. The other sparkling wines also come in sparkling wine bottles. And are labeled Cava, Prosecco, Three Choirs Special Reserve, or whatever.
Personally, I much prefer actual parmesan to other (even very similar) Italian cheeses, but am not a fan of most champagnes. So I'd say that the PDO-style accurate labeling was a net positive to me as a consumer, leaving aside the economic protectionism bit.