The ongoing exodus of EU nationals since the Brexit vote has led to more than a third of businesses fearing they would eventually become unviable.
According to a report by the Food and Drink Federation (FDF), 36 per cent said they would become unviable if they had no access to EU workers.
Seventeen per cent said they would consider relocating outside the UK if that turned out to be the case.
The FDF report is based on research from 627 businesses, including grocers and food retailers, and included input from the British Retail Consortium (BRC) and the National Farmers’ Union.
Two million EU nationals work in the UK, with one fifth of them found in the grocery, food and drink sectors.
The report also said the supply chain would endure “significant disruption” if there were a sudden halt in EU workers coming into the industry.
The BRC added that a sudden drop in EU nationals employed by food retailers could affect product availability and cause prices to rise.
Forty-seven per cent of the businesses surveyed said EU nationals were considering leaving the UK due to the Brexit-induced uncertainty about their residency status.
Thirty-one per cent said they had already seen EU nationals leave since the Brexit referendum took place in June last year.
“EU workers are key to getting British food on our shelves,” BRC sustainability direct Andrew Opie said.
“From producing food, through transport to colleagues in store, they are vital in providing the service and quality British consumers demand.
“To deliver a fair Brexit for consumers and tackle uncertainty, EU colleagues currently working in the retail industry and the wider food supply chain need further clarity about their status once the UK leaves the EU.”
A Government spokesman said: “After we leave the EU we must have an immigration system which works in the best interests of the UK.
“Crucial to the development of this will be the views from a range of businesses, including the agricultural, food, drink and manufacturing sectors.
“We will be setting out our initial proposals for this system in the autumn but we have already been clear there will be an implementation period after we leave the EU to avoid a cliff edge for businesses.
“In June we published our offer to protect the rights of EU citizens in the UK, confirming no-one living here lawfully will be asked to leave when we exit the EU and they will have a grace period to regularise their status.”