The poll, based on responses from 1,051 employers, finds U.K. employers are struggling to fill jobs in factories and hospitals as more EU nationals feel increasingly uncertain over their right to work.
"Almost three-in-ten employers say that non-U.K. nationals from the European Union considered leaving their organization in the six months to December 2016," according to the survey, released Monday.
In the foreword, John L. Marshall, chief executive of The Adecco Group, argued the effects of Brexit were now beginning to take hold.
"The report demonstrates that businesses are struggling to match the right vacancies with the right candidates, with labor and skills shortages caused by a drop in the supply of EU nationals."
Marshall said more than a quarter of businesses said they would "be willing to pay the difference" to secure EU workers if migration restrictions drove up costs.
The most recently available official government statistical data has also suggested a slowing up in the number of EU arrivals.
The number of non-UK nationals working in the U.K. rose by 221,000 to 2.26 million in the 12 months to September, but post-Brexit vote, the last quarter showed an increase of just 30,000.
Another fresh survey is revealing a fall in the number of finance vacancies in the City of London.
The London Employment Monitor, has highlighted a 81% increase in jobs available in January but that figure is considered a disappointment, according to report author Hakan Enver, operations director at Morgan McKinley.
"If the January jobs surge isn't in the triple digits, something's off.
"Until the terms of Brexit are known and put in motion, the jobs market will remain cautious," he said in a press release Monday.
In January 2016, there had been a 115% increase in jobs, month-on-month.