The Telegraph also understands that Matt Hancock, the Health Secretary, has also privately expressed frustration that testing may not be being carried out at full capacity and has ordered any excess tests to be used on NHS staff.

NHS England chief executive Sir Simon Stevens said roll-out of testing will begin this week after staff were sampled on Saturday and Sunday.

On March 11 the UK announced it had carried out 25,000 tests in total and was aiming for 10,000 a day — a target it has yet to reach. Ministers are hoping that a new antibody test that discovers whether a person has previously contracted the virus will be ready within weeks.

Food delivery company Ocado has ordered 100,000 Covid-19 testing kits for staff but has promised to hand them over to the NHS if required.

It has paid £1.5m for the testing kits, with 40,000 already delivered and a further 60,000 to come, while celebrities have been paying up to £375 to have tests done privately.

But experts yesterday questioned why Britain was lagging so far behind other nations in mass testing of the population. Professor Graham Medley, chair of SPI-M, the Scientific Pandemic Influenza Group on Modelling, which advises the Government, said the country simply did not have enough “people and machines” to ramp up capacity, compared to other countries.

“It’s the difference between cooking and catering,” he told the Telegraph. “We might have the brilliant minds but we don’t have the machines or the number of trained people to ramp this up properly.

“We are trying to do things that are beyond any single research laboratory. We need more PCR machines which are expensive and need to be maintained.

“We need the people trained to run them, even though in an ideal world they might never be needed.

“South Korea have got warehouses full of testing kits and machines, and lots of people trained and ready to go. When Sars and Mers came along, they knew they needed it.