Mike McClendon, president of international operations for Lineage Logistics, said its 15 facilities in the UK are more than 90 percent full.

"In three to five weeks you could see the overflowing of frozen and chilled volumes at our facilities. We have concerns right now that volumes need to continue to flow," he told Reuters.

He did not say what would happen if 100 percent capacity was reached. But the impact is expected to be felt on the producers, who would either have to cut production or get rid of excess stock that they cannot store in warehouses.

This is the latest flurry of business for Lineage Logistics after its warehouses filled up last year with food stocks amid fears of shortages ahead of Britain's exit from the European Union, with capacity exceeding 90 percent again.

After the December election of Boris Johnson, when after years of uncertainty it became clear that Britain would leave the trading bloc, as it did on 31st January, capacity dropped to 85 percent, which the company said is a more normal level.

In late February, stocks started rising again and pushed capacity to over 95 percent, it said.

Its cold storage facilities in the UK were already storing greater supplies of pork than usual due to a slump in demand from China, the world's top consumer of the meat, since the start of the year, McClendon said.

Now with the UK in an extended lockdown imposed to rein in the spread of the coronavirus, suppliers of fresh meat and vegetable for restaurants are accumulating stocks because they have no avenues to sell them, he said.

"We see pork, chicken stocks piling up ... and while in the initial weeks of coronavirus, outbound volumes of frozen veggies and frozen meals were rising, now you are seeing inbound volumes exceed outbound volumes," said McClendon.

Capacities are tight in the Benelux region and elsewhere in continental Europe, he said, but conditions in the United Kingdom were most dire.

The Novi, Michigan-based company, owned by investment firm Bay Grove LLC, is the largest temperature-controlled warehouse operator in the world, owning about 48 million cubic metres of space.