A stockpiling frenzy has swept across the United Kingdom as businesses and families frantically prepare for the growing prospect Britain will crash out of the European Union in March.

Businesses have been loading up on spare parts and raw materials amid fears there will be lengthy delays at the border and the government has told drug makers to stockpile enough medicine to cover a six-month shortage. The situation is so serious that on Friday, Health Minister Matt Hancock said the department was drafting plans to charter airplanes to fly in medicine and ration the amount of drugs pharmacies can dispense.

Open this photo in gallery The Davies Turner Logistics warehouse in Bristol, U.K. Jon Rowley/Jon Rowley

Many families have also started hoarding as much food and medicine as possible. “I’m actually terrified to be honest,” said Joanne Elgarf, who lives in London with her husband and three children. She has been buying extra non-perishable items such as pasta, coffee and tuna for a while and has enough supplies to last a month. “I’m quite worried about panic in February and March and people going, ‘Oh my God, this is real, this is going to happen,’ ” she said. Ms. Elgarf is particularly worried about access to the drugs that her four-year-old daughter takes for severe epilepsy. She has enough to cover an extra few weeks but she doesn’t know what will happen if shipments from the EU are disrupted.

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Ms. Elgarf is among 2,500 people who have joined a group called 48 Percent Preppers, which takes its name from the 48 per cent of voters who did not support Brexit in the 2016 referendum. The group shares ideas on how to get ready for a “disastrous Brexit” which could “involve things such as: food shortages, raging inflation, collapsing pension values, seizure of property, increased crime, mass unemployment, collapse in house prices, shortage of medicine,” according to the group’s Facebook page.

Prime Minister Theresa May has insisted that the government is preparing for all eventualities and says she’s convinced Britain won’t face a hard Brexit. But her proposed Brexit agreement with the EU has run into fierce opposition and members of Parliament are expected to soundly reject it in a vote on Tuesday. No one knows what will happen next and that’s led to mounting concern Britain will leave the EU on March 29 without any arrangements for trade or other matters.

With a no-deal Brexit looming, many companies have been scrambling to stockpile essential supplies. Rolls-Royce PLC and Airbus have started stocking up on engine components; Premier Foods is spending £10-million ($17-million) on an inventory of ingredients for cakes, gravy and other products; Imperial Brands has budgeted £30-million to pile up on cigarettes; Irish dairy company Ornua is building a mountain of cheese and high-end retailer Fortnum & Mason has bought a two-month supply of champagne.

“I just wouldn’t like to run short of champagne for the Chelsea Flower Show,” Fortnum chief executive Ewan Venters told journalists last week, referring to the annual event that takes place in May. Over all, British businesses are expected to stockpile around £34-billion worth of goods in the run-up to March 29, according to the London-based Centre for Economics and Business Research.

I just wouldn’t like to run short of champagne for the Chelsea Flower Show — Fortnum chief executive Ewan Venters

Most business leaders and economists fear a no-deal Brexit could cause chaos and shortages because Britain will abruptly lose unfettered access to the EU. The Bank of England has said that a disorderly Brexit could shrink the economy by 8 per cent within a year, drive down house prices by 30 per cent and lop 25 per cent off the value of the pound. Manufacturers and retailers who rely on just-in-time delivery of supplies say a hard Brexit could cause crippling border delays, particularly at the Port of Dover and the Eurotunnel, which together handle around 16,000 trucks a day. A delay of 10 to 30 minutes at customs could bankrupt 10 per cent of British businesses that have EU suppliers, according to a recent survey of 804 companies by the Chartered Institute of Procurement and Supply.

Just a two-minute delay at the Port of Dover could cause traffic on the nearby M20 motorway to back up 27 kilometres and Kent County Council, which includes Dover, said on Friday that it will have to cope with traffic jams involving 10,000 vehicles. The council warned the traffic disruptions could be so serious it will affect other services, such as garbage disposal, school programs and moving bodies to the morgue. There have been reports the government is considering hiring ships to transport goods across the English Channel and line the M20 near Dover with hundreds of portable toilets to provide relief for motorists stuck in traffic.

“All of this is massively disruptive and very scary,” said Ian Wright, chief executive of the Food and Drink Federation, which represents around 7,000 British businesses. “Our members are very concerned.” Mr. Wright said Britain already had a shortage of warehouse space because companies have finely tuned their supply lines so much they rarely keep anything extra on hand. Companies “will only buy what they are intending to use and, by and large, they’ll only make what they know they can sell,” he said.

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Finding storage space won’t be easy. The warehouse vacancy rate across the country has sunk to around 5 per cent, the lowest on record, and in London it has dropped to 3 per cent. “Our warehouses are quite full,” said Philip Stephenson, chairman of Davies Turner PLC, one of Britain’s largest logistic companies, which operates 20 regional warehousing centres, including a facility in Bristol that can hold 27,000 pallets. Normally warehouses empty out at this time of year as products are shipped to stores for Christmas. But Mr. Stephenson said Davies is fielding more calls from companies in Britain and Europe looking for storage because of Brexit.

“It’s just people who want to keep going during the critical days if there’s a sort of hiatus on the 29th of March,” he said. He added that like many businesses, Davies is hoping that some kind of Brexit deal will be struck so that a no-deal scenario can be avoided. “We hope there’s a good enough deal, and I don’t see why there shouldn’t be, so that the U.K., which in many ways has advantages, can continue to act as a gateway to Europe.” He laughed and added: “You Canadians are sitting pretty.”