Testing for healthcare staff should not be on a “first come, first served” basis, the British Medical Association said, after slots offered to key workers ran out for the third day in a row.

More than 10 million essential workers and their households are now eligible for Covid-19 checks as officials race to hit their 100,000-a-day testing target.

But as of 10am on Sunday, home testing kits for England were listed as “unavailable” on the Government’s website – two hours after booking slots reopened.

Following its launch on Friday, slots for both home-testing and drive-through centres in England have been used up within the first few hours.

Drive-through tests in Scotland were the only option currently still available on Sunday evening.

Dr Chaand Nagpaul, chairman of the British Medical Association (BMA) council, said that the online booking system “offered no practical help” to healthcare workers.

“There is no point putting forward a proposal unless its matched with adequate capacity,” he told the PA news agency.

“What we found in the first two days was that within an hour the bookings had all been taken up, and therefore offered no practical help for large numbers of healthcare staff, who found the website had effectively closed to bookings.

“If the Government wants healthcare workers to have access to the test, it has to be in the context or providing adequate capacity, not a ‘first come first served’ and closing within an hour.”

He added: “That’s not delivering on the needs of our health and care staff.”

Dr Nagpaul said that the current testing capacity is “well, well short” of the number of healthcare staff who are currently self-isolating, as he called on the Government to go further than the target.

“Our estimate is that there are about 90,000 health and care staff self-isolating based upon the Government figures of absence rates,” he told PA.

“With that in mind, if they all wanted to have a test, clearly capacity has to match that number on that assumption.”

Some 46,000 people tried to book a coronavirus test on Friday, but, within two minutes of the website going live at 6am, all 5,000 tests for people to carry out at home had been booked.

Under the expansion of the testing, NHS and social care staff, police officers, teachers, social workers, undertakers, journalists and those who work in supermarkets and food production are among those now eligible.

Test booking slots or home testing kits will become available from 8am each day, the Department of Health and Social Care (DHSC) has said, with their release staggered throughout the day.

The Government is “working hard” to increase the availability of Covid-19 tests through the online service, according to a DHSC spokeswoman.

“There has been significant demand for booking tests,” the spokeswoman said.

“It is great that so many essential workers want to get tested and get back to work to help the national effort against coronavirus.

“We are working hard to increase the availability of online booking slots, which is determined by a number of factors including overall capacity of the testing system and how many test kits we send to those most in need, for example in care homes.

“It is also fantastic that we have received requests for 5,000 home kits on day one of the online portal being available.”