Milk and More, the largest such service in the country, said it had added 25,000 customers and now needs 100 new workers.
Local milk deliverers have also said demand has surged as people try to limit visits to their local shop or supermarket.
Colin Henderson, who's been a milkman for 40 years, said: "The milk has gone berserk.
"I have got a pile of notes from customers and my round is taking an extra hour every day now. The dairy I work with said it is just manic."
The 56-year-old from Chester-le-Street, County Durham, said: "I just hope that after this is finished that people stay with us.
"I have people ringing all the time, emails from head office, and it's great, but it would have been better when I was 25."
Milkmen and their electric floats were a familiar sight in the UK for decades, dropping off and collecting milk bottles on their early-morning rounds.
However, their numbers dwindled dramatically due to competition from supermarkets.
Milk & More still employs 1,000 milkmen and women and uses the latest electric floats to deliver around 100 million one-pint bottles a year.
The firm's boss, Patrick Muller, said: "We have been at the heart of the communities in which we serve for decades, but potentially we have never had such an important role as we do now in this current health crisis.
"Our customers are our number one priority, and they're relying on us delivering to them more now than ever before, which is why it is absolutely crucial that we look to increase our workforce."
He urged anyone out of work - permanently or temporarily - to contact the company.
Prince Charles' farm, Home Farm Highgrove in Gloucestershire, also said it had been very busy after it recently installed a vending machine for its organic milk.