Coronavirus tests for key workers through the government’s new booking website have run out quickly in England for a second consecutive day.

More than 10 million key workers and their households are eligible for Covid-19 tests as the government attempts to deliver its pledge of 100,000 tests a day by Thursday, but home-testing kits for people across the UK and slots to visit testing centres in England and Northern Ireland were quickly taken up on Saturday morning.

The BBC reported that home-testing kits had become unavailable after 15 minutes on Saturday morning, and tests at regional drive-through sites in England were booked up within an hour. Drive-through tests in Scotland remain available, and the Welsh government is developing its own portal and has asked that the central booking system does not take bookings for the country’s testing sites.

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A spokesman for the Department of Health and Social Care said more test booking slots or home-testing kits would be made available from Sunday morning at 8am.

A total of 46,000 people tried to book a coronavirus test on Friday, but all 5,000 home tests had been allocated within two minutes of the website going live at 6am. Within three hours of the site launching, all applications had closed.

More than 15,000 appointments for tests at drive-through centres also ran out before midday forcing the DHSC to apologise on Twitter.

Asked how many tests were available on Saturday, NHS England’s medical director, Prof Stephen Powis, told BBC Breakfast: “We are going at capacity, over 50,000 now. The aim is to get to 100,000 by Thursday.

“The NHS has committed to capacity of 25,000 within NHS laboratories and we are on trajectory for that capacity to be in place.”

Dr Simon Eccles, the chief clinical information officer for NHS England, tweeted: “Home kits all booked by 8:15! I know it’s frustrating but we’re developing more lab, supply and logistics capacity every day.

“If we’d waited until we had the full 100k, to launch, no one would have had a test today. More home kits again tomorrow, even more next week.”

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

However, even those who manage to book a test have said they were turned away after arriving at drive-through centres.

Key worker Natalie Orton-Rose, from Leicester, said she had been self-isolating after being told by her doctor that it was likely she had coronavirus and booked a test on Friday morning.

“I drove an hour from my home in Leicester [to the test centre in Nottingham] and sat waiting for half an hour in the queue only to be told actually they had no more tests left,” she told the BBC.

“I am absolutely disgusted. It is bad enough that my closest test centre is an hour away but then to waste my time and fuel … I think the government and public need to be aware that just because you have an appointment and turn up doesn’t mean you’ll get the very much needed test.”

• This article was amended on 26 April 2020. An earlier version incorrectly described Dr Simon Eccles as chief clinical information officer (CCIO) at NHS Digital. In fact he is CCIO for health and care across the Department of Health and Social Care, NHS England and NHS Improvement.