Belgian potato processor Agristo is running out of places to stash its french fries. With its own freezers full up and hardly any space available to rent, the company was forced to cut daily output by about 20%.

Demand for cold-storage space has surged after bars, restaurants and sports venues closed, leaving their suppliers hunting for new customers or somewhere to store the unsold food. Products like vegetables and meat that are usually sold fresh are now competing with frozen food staples for the same storage space.

“Once you cannot put any more food in cold storage you simply have to stop production,” said Agristo Chief Operating Officer Kristof Wallays.

The cold-storage squeeze is yet another way that the coronavirus is wreaking havoc on the global food industry. From empty meat shelves in the U.S. and growing levels of hunger in Africa to convicts filling in as farmworkers and surging demand for avocados, food-supply chains are being upended across the world.

Farmers, manufacturers and retailers in Europe say it’s near-impossible to find fridge and freezer space. The shortage is forcing production cuts, and may mean wasting thousands of tons of produce that suddenly has nowhere else to go.

Exports have also been disrupted as international demand dropped and port holdups in China led to a shortage of empty shipping containers. That’s meant food supposed to be shipped around the world is stuck clogging up freezers at home.

Lineage Logistics, the world’s largest temperature-controlled logistics provider, estimates that more than 90% of its cold-storage facilities in Europe are already full.

“We are at a critical point now to make sure the supply chain keeps moving along,” said Mike McClendon, president of international operations and executive vice-president for network optimization.

In the U.K., there’s barely any room left at all, according to Shane Brennan, chief executive of the Cold Chain Federation. Pressure is going to start building as the British lamb season starts, and get worse when farmers harvest fresh produce later in the year, he said.

“If you are a business looking to find storage for your product in the U.K. cold chain right now, then you are not going to find it,” said Brennan. “U.K. cold storage facilities are essentially full and they’re not taking on any new business.”

There may be some relief in sight as governments begin to lift lockdown measures and refrigerated containers return from China, according to the Global Cold Chain Alliance, a trade association representing the industry.

“We hope the reopening of activities in economies across Europe will release stock, but nobody can say how things will evolve,” said Julie Hanson, European director at the Global Cold Chain Alliance. “Governments are easing measures right now, but what happens if there is a second wave of coronavirus and we have to go back to containment?”

In the meantime, producers are looking for other solutions. Farm groups have been promoting in-home steak nights to encourage consumers to splash out on premium cuts of meat.

“We can’t produce new cold storage units that quickly, it’s just not feasible,” said Ellie Phipps, policy officer at the U.K.’s National Sheep Association. “As far as we’re concerned the best thing to do now is to try get people eating it rather than freezing it to try get it out of the way.”