Attempts to boost the number of ventilators and coronavirus tests have stalled, new figures show – even as the UK threatens to overtake Italy’s worst daily death toll.

Just 16,094 tests were carried out on Tuesday, including 3,680 on NHS staff and their families, around the same figure as on Sunday and far short of the pledge of 100,000 in just three weeks’ time.

And the NHS still has only 11,500 ventilators, including 1.500 “on order”, Downing Street said – way below the 18,000 Matt Hancock said were needed for the coronavirus peak.

However, a No 10 spokesman dismissed suggestions of problems looming, insisting: “The target remains very firmly to achieve 100,000 tests a day by the end of the month.”

On the situation on hospital wards, he said: “We continue to have spare critical care beds and ventilators.”

The position was revealed as Downing Street said Boris Johnson “continues to improve” while still receiving oxygen in intensive care – but declined to say if he has been in contact with anyone other than hospital staff.

For the first time, No 10 said the near-certain decision to extend the lockdown would be taken without him, led by Dominic Raab instead.

“The prime minister is not working, we are very clear on that. He has asked the first secretary of state to deputise for him,” the spokesman said.

“It will be first secretary of state who leads the Cobra meeting today and the first secretary of state who will lead any cabinet decision-making process.”

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The comments came as Downing Street rebuffed Keir Starmer’s call for it to publish an “exit strategy” from the crisis, as a longer lockdown looms.

“Work is of course underway, but what we should be focused on now is stopping the spread of the disease while building up the capacity of the NHS, because that is the way to save lives,” the spokesman said.

And he played down suggestions of extra lockdown powers, requested by some police forces fearing public disobedience over the long, sunny Easter weekend.

“For now, our process is on ensuing the steps we have in place are properly enforced,” he said.

However, No 10 threw its weight behind the Northamptonshire chief constable, who suggested roadblocks – and even searches of shopping trolleys – might be necessary to keep people in check.

“We have given them a job to do and they will use their own discretion as to how best they do that job,” the spokesman said, when asked if roadblocks and trolley searches were acceptable.

‘The police have our full backing ... that is the nature of policing in the United Kingdom.”

Mr Raab was preparing to chair a Cobra meeting to agree a common approach to the lockdown, as Wales and Scotland push hard for an extension – beyond next week’s expiry date – to be confirmed now.

The spokesman said he was not “contradicting” Nicola Sturgeon’s warning that there is no possibility of any relaxation of restrictions at this point.