The British Poultry Council has said food producers are facing serious staff shortages because of Brexit as this week’s partial closure of the Nando’s chain threw the spotlight on problems made worse by the fallout from Covid.

The trade association said its members, which include 2 Sisters Food Group – the country’s largest supplier of supermarket chicken, said one in six jobs were unfilled as a result of EU workers leaving the UK after Brexit.

There have already been warnings of turkey shortages this Christmas as shortages of delivery drivers, abattoir staff and other workers drive up pay and other costs.

The British Poultry Council’s chief executive, Richard Griffiths, said the group had written to the home secretary, Priti Patel, this month asking for the government to relax immigration rules but had not yet received a response.

Last week KFC said supply chain issues were disrupting their food and packaging stocks nationwide. Supermarkets have also been struggling to fill shelves amid a serious shortage of HGV drivers.

“We’ve seen a loss of staff across the supply chain, particularly in our member companies,” Griffiths said. “Our members are reporting up to 16% vacancies at the moment as a direct result of the limiting of immigration policies, and we are asking the government to ease those and look at skills and development.”

In July, Ranjit Singh Boparan, the billionaire founder of 2 Sisters, said the “pingdemic” – which forced large numbers of healthy workers to self-isolate after being “pinged” by NHS test and trace – simply masked an industry already at crisis point owing to Brexit-related labour shortages.

Within its 16,000-member workforce, the majority of whom work in its chicken and ready-meal production facilities, 15% of jobs were unfilled. Brexit had “acutely reduced available workers across the food sector” with entry level jobs hardest to fill, 2 Sisters said. The company was also grappling with the soaring cost of ingredients, wage inflation and Covid-related absences, he said.

“The critical labour issue alone means we walk a tightrope every week at the moment,” said Boparan, who warned that without government help food waste would rocket “simply because it cannot be processed or delivered”.

The British Poultry Council said increasing wages to attract domestic workers was not the answer. The industry’s experience in recent years had been that the “willingness and availability is just not there within the UK workforce”, Griffiths said.

“We operate in areas that have generally high employment so the availability of UK labour is just not there,” he told the BBC, pointing to the staff problems in the hospitality trade as well as the chronic shortage of HGV drivers.

“We are just one part of the supply chain and this is affecting everybody. We are not alone here. This is a massive problem that needs addressing across the industry and the government needs to acknowledge the problem.”