One of the few dairies allowed to make Stilton said it has had to stop sales to the European Union (EU) since Brexit.
Hartington Creamery at Pikehall, Derbyshire, said the paperwork needed for each order was costing too much.
It added, however, that sales have “surged” in the US and Canada.
The government said it was working closely with traders adjusting to the new arrangements.
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