Canada says it wants to protect the domestic dairy industry by preventing further imports of British cheese.
But the United Kingdom is asking Canada to give greater access to British varieties of cheese, such as Stilton and Wensleydale.
The U-K and Canada have started talks on a free-trade deal, including about greater co-operation on renewable energy, technology and the digital economy.
But Canada says Britain cannot have an extra quota for its cheese, because Canadian dairy farmers might suffer as a result.
Canada produces one-thousand, four-hundred and 50 varieties of cheese including Oka, a semi-soft rind cheese, originally made by Trappist monks in Quebec.
Canada's Trade Minister Mary Ng says the U-K is an important trading partner and a free-trade deal will benefit Canadian and British businesses.