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This article is part of a Fortune Special Report: Business in the Coronavirus Economy—a look at the impact of the pandemic on more than 50 industries.

Online shopping was supposed to be a panacea for those forced to self-isolate owing to coronavirus symptoms, or because their age or underlying health conditions made them especially vulnerable.

But, so far, it hasn’t quite worked out as techno-optimists envisioned.

With most of Britain’s population stuck at home because of work-from-home policies, or self-isolating owing to suspected coronavirus infections, the region’s online grocery firms are struggling to keep pace with the sudden surge in demand for their services.

Online grocery delivery was already far more popular in Britain than in many other countries: It accounts for about 7.3% of grocery spending in the U.K., third only to South Korea and Japan. By contrast, in the U.S., the market share for online shopping is less than 2%, according to market research firm GlobalData.But with the coronavirus pandemic, demand for online groceries has skyrocketed, with grocers reporting higher order volumes than even during the Christmas season.

Not only are many more customers ordering online than usual, but the average order sizes have increased as well, as customers panic-buy and stockpile, the supermarkets report. That has made it even harder for grocers: Larger orders take more time to fulfill, and they’ve struggled to maintain adequate stocks of popular items such as toilet paper, hand sanitizer, canned food, UHT milk, and dried pasta.

Most grocers allow online customers to choose a one-hour delivery time slot, usually between about 7 a.m. and 10 p.m. But with the sudden spike in demand, customers have found open slots almost impossible to find, even looking as far out as three weeks. Others have complained about delivery times slipping—or grocers canceling already booked orders altogether. A few online grocers were so inundated they had to stop taking new order altogether.

In response, a number of grocery stores announced on Wednesday that will now begin to prioritize people over 70, the disabled and those from other vulnerable groups, for delivery slot bookings.

Tesco, one of the country’s largest supermarket chains, has recommended customers concerned about the difficulty of finding an online delivery slot return to shopping in its physical stores, provided they are not part of a vulnerable population.

Sainsbury’s, another large British grocer, announced on Wednesday that it will open an hour early on Thursday, March 19, just for people aged 70 and over.

The grocer was among several announcing that they will now impose strict limits on the number items customers can purchase, limiting them to just two of the most stockpiled items, such as packets of toilet paper and dried pasta, and just three of any grocery item.

Sainsbury’s and Waitrose, an upmarket grocery chain owned by retailer John Lewis, said they would close some separate in-store services, such as the separate butchery and cheese counters, to make more staff available to restock depleted shelves. And Waitrose has recruited staff from its head office, and from elsewhere in the John Lewis, to help staff its stores and fulfill online orders.

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Ocado, a popular online-only grocer that launched in 2002, has seen the volume of traffic on its website increase as much as fourfold since the beginning of March. “It’s the peakiest peak we’ve ever experienced in the history of the business,” says David Shriver, Ocado’s group head of communications.

The company had so many orders that last weekend it had to stop taking registrations from new customers so that it could prioritize service for existing ones, Shriver adds.

To try to slow the tide of orders, Ocado also took its mobile app out of service and introduced a system where even those trying to place orders on its website are placed into a “virtual queue.” This means customers have to wait on a holding page before they are allowed to access the main website to do their online shopping.

On Monday, some Ocado customers complained on social media that this wait time could be as long as 15 minutes at peak hours. Waitrose, an upscale U.K. supermarket chain, imposed a similar queuing system as well.

But, even with these steps, the companies’ systems strained under the enormous volume of demand. By Thursday, Ocado was forced to suspend taking all orders, even for existing customers, until further notice. Riverford, a company that sells organic produce online, also had to stop processing new orders owing to high volumes. Waitrose’s website crashed periodically, and the company said it was working hard to keep it functioning normally.

Ocado says it would ramp up staffing to try to meet increased customer demand. Although the company uses robots to help move groceries around its warehouses, the actual selection of individual customer orders is done by humans, as is, of course, the delivery.

Around the world, other e-commerce companies are facing similar pressures to add employees to meet a coronavirus-related wave of demand. Amazon said its customers in the U.S. were facing “longer than usual” delivery windows as popular products were selling out.

The company announced Monday that it will try to hire an additional 100,000 full- and part-time workers in the U.S. to staff its warehouses and help deliver orders. It also said it will raise its minimum wage to at least $17 an hour through April.

“Our labor needs are unprecedented for this time of year,” Dave Clark, Amazon’s senior vice president of worldwide operations, said in a blog post Monday.

U.S. supermarket chain Kroger also said it was hiring across its retail stores and distribution centers, with the aim to get new workers on the job within days and weeks.

Even in countries that have imposed mandatory quarantines, workers in grocery stores and food delivery have been exempted as governments try to make sure people can still get the food they need without exposing themselves or others to potential infection.

This story was updated on March 18, 2020, to reflect new measures grocery stores have announced to try to counter hoarding, meet surging demand, and prioritize the needs of vulnerable and shoppers over the age of 70. It was also updated to include the news that Ocado had been forced to cease taking order entirely.