There is absolutely no chance that the EU’s proposed trade deal with the US, known as TTIP*, will allow American products to be marketed in the UK or anywhere else in the EU as Cornish pasties, Cumberland sausage, Stilton or any other currently protected name**.
Some 60 UK products are protected under three linked EU schemes that allow producers to use the name on EU markets only if they are making the products within the traditional production regions and/or using full traditional recipes.
The TTIP deal with the US, currently under negotiation, may extend to US markets the protection against non-genuine rivals that traditional producers already enjoy here in Europe.
That is what the negotiations are about. There’s no question at all of weakening the existing protection for recognised EU products on the EU market. The European Commission will simply not agree to that. And trade deals anyway need to be ratified by national governments and the European Parliament, who also would not agree to weakening existing safeguards.
Under the recently concluded CETA deal with Canada, there is again no provision that could possibly permit Canadian producers to use the UK names currently protected in the EU. There is a mechanism for EU products, including those from the UK, to get enhanced protection on Canadian markets. Some, such as Scotch Whisky, are already protected there under other global arrangements.
A full, searchable list of protected products is here
*TTIP = Transatlantic Trade and Investment Partnership