The number of EU nationals leaving Britain, most of them from central Europe, rose by 33,000 to 122,000 people during the 12 months to March, according to the latest data following last year's Brexit referendum.
Franco Manca's parent company, Fulham Shore, said the prospect of new controls on immigration when Britain leaves the bloc was "already affecting the availability of skilled European restaurant staff".
The company, where only 20 per cent of the staff are British, said it was implementing "a number of incentive schemes" to persuade Europeans to stay.
The hospitality industry currently has the highest proportion of unfilled jobs in Britain, according to the Office for National Statistics (ONS).
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And the situation is worsening, with 4.3 per cent of hospitality jobs vacant in June to August 2017, compared with 3.5 per cent a year earlier.
Alex Wrethman, the head of Charlotte's group of bistros in west London, said EU nationals were being put off by the sharp fall in the value of the pound against the euro since the Brexit vote.
Wrethman said he struggled to find Britons who were as committed to the job as their European colleagues.
"It's difficult to find a British person to get out of bed to wash dishes," said Wrethman, who started working in the restaurants he now owns as a teenager.
"It's tied up with something historic. It's a class thing," Wrethman said.
On a break from chopping avocados and smoked salmon for brunches, the head chef of Charlotte's newest restaurant complained of a "bleak time for the industry", where he thinks his British background and willingness to work long hours make him a rarity.
"I genuinely believe the industry is two or three years away from imploding."
Leaked government proposals for restricting the stay of low-skilled EU workers to just two years, would be "catastrophic" for the industry, according to trade body, the British Hospitality Association.
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