This is because all warehouse space or chilled and frozen storage has been reserved for Christmas products, meaning suppliers cannot stockpile or ramp up production in anticipation of delays in food imports getting across the border.
Food imports are also usually at their peak in late autumn, but the government estimates that for months ports will only be able to handle up to 60% of the traffic that currently passes through, according to the FDF.
This could leave British shoppers having to turn to the likes of turkey, stuffing and pigs-in-blankets as regular fresh food supplies run low.
FDF chief executive Ian Wright told HuffPost UK: “The peak Christmas production period and the UK’s frozen and chilled warehousing space has been reserved for Christmas production for two years or more.
“This peak production period also means many manufacturers will also lack the capacity to increase production even if storage was available.
“With imports at their annual peak and port capacity significantly diminished, we will see random and unpredictable shortages of both produce and raw materials.
“This will translate into random shortages on shelves and production lines being shut down where key just-in-time ingredients fail to arrive.
“As a result, products in storage for Christmas may have to fill these gaps.”
Wright also expressed concern at the government’s plan for a “light touch” approach to border checks to keep trade flowing as freely as possible if there is no deal.
The government has said there will be no new border checks for food coming in from the EU.
But Wright warned this could create a “smuggler’s charter” which could see criminals importing cheap food into the UK from the rest of the world via the EU, where it will not be checked if it is bound for Britain, which could flout safety standards and could threaten public health.
“It’s not just white-van man bringing more cheap fags over the border, it means substandard produce being put into the UK market,” he said.
“These things started with people cutting corners on food safety and they end with someone dead.
“And it means the UK food and drink industry’s reputation is destroyed.”
Michael Bell, of the Northern Ireland Food and Drink Association, suggested the land border with the Republic of Ireland could be particularly vulnerable.
He pointed out past incidents, including the 2008 pork crisis – in which contamination lead to an international recall of pork products from Ireland – showed what could go wrong.
“If we create a situation the border which causes a rise in criminality because we’ve invented complicated border systems which are not policeable, we will then have a loss of public trust and that is potentially the most damaging thing.
“So our view is that frictionless at the cost of integrity is not a price worth paying.”
The government is reviving plans to charter ferries to bring in food across the Channel and alleviate pressure on ports like Dover, but these ships will prioritise medical supplies in the event of no deal.
Work is also ongoing to keep borders as open as possible.
A department for environment, food and rural affairs spokesperson said: “We will always back Britain’s great farming and food industry, and the government is boosting its preparations for a no-deal Brexit to ensure there is as little disruption as possible to our national life.
“We have a highly-resilient food supply chain and consumers in the UK have access to a range of sources of food. This will continue to be the case whether we leave the EU with or without a deal.”