Downing Street is under fire after refusing to guarantee an independent inquiry into its handling of the coronavirus pandemic, despite mounting criticism.

Dominic Raab agreed there would be “lessons to be learned” when the crisis is over – but ducked a call to ensure a judge is appointed to explore what mistakes might have been made.

The stance was later echoed by Boris Johnson’s spokesman, raising suspicions that ministers are reluctant to see an Iraq War-style probe held.

One analysis now suggests the real death toll from coronavirus in the UK is already above 40,000 – twice the total once described by an NHS chief as “a good result”.

Mr Raab came under pressure in the Commons from Ed Davey, the acting Liberal Democrat leader, but the stand-in prime minister replied: “I won't take up his offer of committing to a public inquiry.

“I think that there are definitely lessons to be learned and, when we get through this crisis, it will be important that we take stock and we come together to understand with an unprecedented challenge on an international scale what can be done to avoid it happening again.

“But I think right now, from our key NHS frontline workers to the members of the public, they would rightly expect our full focus to be, as we come through the peak of this virus, to make sure that we save lives, protect the NHS and steer the whole country through this crisis rather than engaging in that process or that set of deliberations right now.”

Speaking afterwards, Sir Ed said: “It is deeply concerning that the government are avoiding even committing to a future public inquiry into the coronavirus crisis.

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“From the lack protection for frontline health and care workers to the complete mess the government have made of testing, ministers have questions to answer.”

Ian Blackford, the Scottish National Party leader, told The Independent: “When this is over, it is inevitable that there will have to be a review on the government response.

“This is not about pointing fingers or laying blame but simply about the responsibility to review actions taken.”

Caroline Lucas, the Green MP, said: “If tens of thousands of deaths in the first pandemic for 100 years doesn't merit a public inquiry, I don't know what does. Taking stock, as Dominic Raab suggests, doesn't cover it at all.”

And Daniel Machover, a public inquiry solicitor, said: “A public inquiry along the lines of the Grenfell Tower inquiry would be the best way to determine how well the government has handled this crisis.

“Inquiries conducted by civil servants behind closed doors or by politicians on select committees can be beholden to whoever is in power – questions can be withheld and avoided; witnesses can be missed.”

The Chilcot inquiry into the Iraq War invasion was able to take evidence in public from Tony Blair and other architects of the invasion, although it was criticised for taking seven years to public conclusions.

Theresa May conceded a public inquiry into the Grenfell tragedy – but no similar probe took place into the origins of the 2008 financial crash.