Keeping the number of coronavirus deaths below 20,000 will still be “a good result” for the UK, a health chief says, as he urged the public not to become “complacent”.

Stephen Powis distanced the NHS from a new study predicting the UK is on course for 5,700 deaths fatalities – far lower than originally predicted – suggesting it was far too low.

“If it’s less than 20,000, that would be a good result, although every death is absolutely a tragedy,” he told a Downing Street press conference.

And he added: “We shouldn’t be complacent about that. Although that would be a good result, it will only happen if we stop the transmission of the virus.

“It doesn’t happen by luck, it’s not just chance – it’s because of the actions that you take, I take, we all take, to reduce the transmission of the virus.”

The figure repeats the projection made, almost two weeks ago, by Patrick Vallance, the chief scientific adviser.

On Friday, statisticians at Imperial College London said their new best guess for the UK deaths was 5,700 – compared with 28,000 in Italy and around 46,000 in Spain.

But Mr Powis, the medical director at NHS England, said even under 20,000 would only be achieved if people “really lock down and hone down on what we have been asked to do”.

“I cannot emphasise enough. You have the chance to save a life, you have the chance to stop a ventilator being used that otherwise would need to be used. It really is as simple as that,” he said.

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The comments came after it was announced that the number of UK deaths has passed 1,000, with 260 further victims of the epidemic.

Worryingly, the increase, from 759 to 1,019, was by far the biggest day-on-day rise in fatalities since the outbreak began.

More than 120,000 coronavirus tests have taken place, with more than 17,000 positive results, the Department of Health and Social Care said.

At the press conference, Alok Sharma, the business secretary, insisted there were “no gaps in government”, despite Alister Jack, the Scottish secretary, joining Boris Johnson and Matt Hancock in isolation.

The prime minister was still “leading the response from the front”, he insisted, saying he had chaired a videoconference earlier.

Mr Sharma also announced changes to insolvency rules to give firms greater “flexibility” to survive the crisis.

Measures to cut red tape, to allow companies to produce personal protective equipment (PPE) and hand sanitiser more quickly, were also unveiled.

The temporary suspension of rules on wrongful trading would “remove the threat of personal liability” from directors trying to save their companies, Mr Sharma said.