UK produces more varieties. Of course it depends what "great cheese" is defined as - naming is a lot looser in the UK - but a cheese DB without UK (and definitely Italy too) is missing a lot.
I doubt there are many of those named varieties that anyone would truthfully say are low-quality produce by definition, though. There is just a rich, long history of cheesemaking and a wide variety of different cheeses.
Developer here.
As a french I only had access to french cheesemaker, so my database if majority of french cheese
You have to knwo that most French cheese make WONT sold cheese from other country.
If you want italian cheese, you need to go to Italian cheese maker and if you wan cheeddar, you go to mark and spencer :D
Thus most of my dataset are very local french cheese