The Government’s Covid-19 testing website was overwhelmed as it opened to new bookings on Friday, with home testing kits running out in the first two minutes of the site going live.

Up to 10 million key workers and their households in England are now eligible for coronavirus tests if they have symptoms as the Government races to hit its 100,000-a-day testing target by next Thursday.

Under the expansion, 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.

People can register on the gov.uk website for an appointment at a drive-through centre or can request a home test kit, which ran out almost immediately after opening to bookings at 6am.

The PM’s spokesman said: “Within two minutes of the portal opening this morning, 5,000 testing kits had been ordered.

“And that’s the available capacity for today.”

The spokesman said up to 18,000 home testing kits per day will be available by the end of next week.

Another 15,000 tests are anticipated to take place at the drive-through centres on Friday, the PM’s spokesman added.

It came as the Department of Health announced a total of 19,506 patients had died in hospital after testing positive for coronavirus in the UK as of 5pm on Thursday, up by 768 from 18,738 the day before.

Number 10 said the Government is trusting that those applying for tests are key workers, with no eligibility checks in place for online bookings.

The official spokesman said: “As with many other aspects of the coronavirus response, we would expect the public to respond in good faith.

“That is what they have done with other aspects of the scheme, I think we’d expect it to be the same here.”

On testing being rolled out to other groups, the spokesman added: “We want the capacity that we have in the system to be used and you can see this morning that the system is working, people are booking slots and now they are going to be able to undergo tests.”

Asked whether the Government was confident people would be able to test themselves accurately with a kit sent to their homes, the spokesman added: “There are videos available to show people how to do this and people will be given clear instructions.

“We would hope they would be able to do this, yes.”

Health Secretary Matt Hancock, when asked whether he thought the Government would meet the target of 100,000 tests a day by next Thursday, said: “I do, yes, but nothing’s guaranteed in life.”

Under the scheme, test results from the drive-through sites will be sent out by text within 48 hours, and within 72 hours of collection of the home delivery tests.

By mid-morning on Friday, the gov.uk website said it was not accepting any more applications.

It said: “Coronavirus test: applications closed. You can’t currently register for a Covid-19 test. Please check back here later.”

The Department of Health tweeted: “There has been significant demand for booking tests today.

“We apologise for any inconvenience.”

It comes as Mr Hancock said easing the UK’s lockdown depends on the speed at which the number of new cases of Covid-19 falls and that is as yet “unknown”.

The number of new cases is being tracked through hospital admissions, a new testing study in the community with results expected in early May, and data gathered from key workers now being tested, Mr Hancock said.

But he suggested there is no prospect of easing the lockdown yet, and that coronavirus cases need to drop substantially before the next phase of isolating infected people and their contacts can be truly effective.

Through a process of mass testing and by isolating infected people and their contacts, ministers hope that future localised outbreaks of corornavirus can be kept under control.

Mr Hancock told Radio 4’s Today programme: “Now that we’re at the peak, and we very much hope that things will start to slow down and, if and when they do, then the speed with which the number of new cases reduces will frankly will determine how long we need to keep the measures on and that is as yet unknown.”

He said it was not quite the case that mass testing and contact tracing needed to be in place before the current restrictions are eased, but said contact tracing worked better when the number of infections was pushed right down.

“The truth is that we need to get the number of new cases down, right down, and the lower you go, the more effective contact tracing is because the more resources you can put into each individual case that gets a positive test.

“You can really make sure you can get hold of all of their contacts and get them, in many cases, to self-isolate.

“The smaller the number of new cases, the more effective the test, track and trace system will be.”

It comes as:

– US President Donald Trump said Boris Johnson sounded “incredible” and “ready to go” when they spoke on the phone this week, following reports in the Telegraph that the Prime Minister is preparing to return to work on Monday

– The World Health Organisation announced a landmark £6.5 billion programme, backed by the UK, to find safe, affordable and universally available vaccines and therapeutics, as soon as possible

– On Thursday there were 77,000 new claims from businesses to furlough workers – bringing the total to 512,000, Downing Street said

– The Duke and Duchess of Cambridge and their three children joined in the nationwide weekly clap for carers on Thursday evening

Mr Hancock said on Friday that Mr Johnson was “on the mend” but any return to work was a matter for him and his doctors.

He told ITV’s Good Morning Britain: “He’s definitely in good spirits and getting much better and so that is very good news.

“I’m sure the whole country looks forward to him coming out of his isolation.”

It comes as the UK marked a month in lockdown this week, with a review of the restrictions next due to take place on May 7.