Cheddar is a small town in Somerset which I have visited a few times. Corton is a village in Suffolk where my relatives used to live. Corton is also the name of a famous vineyard in Burgundy, and I have drunk a few bottles of Bonneau du Martray myself when it used to be affordable.
Now suppose I own a vineyard in Corton in Suffolk and I label my wine for sale as “Corton”. This is illegal under the law of the European Union because Corton in Burgundy has the prior claim. It goes to market as Corton Appelation d’Origine Protegée (formerly Appelation Controlée) and no one else is allowed to use any similar description. The Corton vineyard is in fact so famous that only the vineyard name appears on the label and there is no mention of the village of Aloxe where it is located (and confusingly the village has changed its name to Aloxe-Corton). The English equivalent of AOP or AC is PGI for Protected Geographical Indication and some cheeses such as Stilton PGI have it.
However, Cheddar does not have it despite the fact that the caves of Cheddar Gorge and nearby Wookey Hole are considered to be good places to mature Cheddar Cheese. It would need to apply for PGI status, and obviously lots of other Cheddar manufacturers, including French manufacturers, would object.
One argument is that “cheddaring” is the name of an industrial process. Well so is “Champagne method” but Corton in Suffolk would not be allowed to put this on the bottle for its sparkling wines since it is also protected.
The best that Cheddar can do is West Country Farmhouse Cheddar PGI and you may wish to look out for it.
On the whole this system is just too political and the British do not get a fair deal out of it, though it can be said that they are the Johnny-come-latelies to the AC system which began in Chateauneuf-du-Pape in the Rhone Valley.
On March 30th 2019 after Brexit, this system could just vanish if there is no agreement reached. Then any vineyard in Britain will be able to put “Corton” on the label unless we adopt our own new system. Since Britain is a major market for French products, this does give us a bit of bargaining power and we will need to wait and see what happens.