A rare British gastronomic hit in France, the Marks & Spencer sandwich may no longer appear on Parisian shelves without a post-Brexit trade deal, the supermarket's chairman warned in an interview published Friday.

Archie Norman told the Financial Times that a no-deal Brexit would spell the "demise" of the sandwiches, which are transported through the Channel Tunnel every day.

"If our lorries are sitting in a lorry park near Dover for half a day, that would be the demise of the great M&S sandwich in Paris," he told the newspaper.

The lunchtime favorites are made in a factory in central England, before being shipped to 1,000 stores in Britain and 20 in France, 19 of which are in the capital.

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The British supermarket sells around one million sandwiches each year in France, but Norman suggested it would not be financially viable to set up a factory in France in the event of a no-deal Brexit.

British Prime Minister Theresa May was on Friday heading to meet French President Emmanuel Macron on the Mediterranean coast to lobby for her Brexit plan, which has so far split her government while failing to win over skeptical EU negotiators.

The prime minister has just a few months before an agreement on Britain's divorce from the EU -- set for March 29, 2019 -- must be forged in order to allow time for ratification before the exit.

The EU has rejected May's proposed solution to keeping the border between the UK and EU member Ireland open without a "hard border", with Bank of England chief Mark Carney warning on Friday that the prospects of a no-deal Brexit were "uncomfortably high".