Trials for a Covid-19 vaccine could be completed by mid-August, a key adviser to the government has said.

John Bell, a member of the government’s coronavirus vaccine taskforce, told BBC Radio 4’s Today programme that human test trials had begun at Oxford University this week.

But Bell emphasised that “the real question” was not when the vaccine would become available, but whether it would be effective.

“[The question is] will it protect people, and that has not been tested and it will only be tested once you have vaccinated a significant number of people and exposed them to the virus and counted how many people have got the virus in that population,” he said.

“But if things go on course and it does have efficacy, then I think it is reasonable to think that they would be able to complete their trial by mid-August.”

Bell said a candidate vaccine being tested at Oxford had gone “into man” for the first time on Thursday, after a wide range of safety studies.

“If we can see evidence of a strong immune response by the middle or the end of May, then I think the game is on,” he said, adding that the next step would then be “the massive issue of how you manufacture at scale many billions of doses”.

The comments came amid mounting pressure on the government to provide personal protective equipment (PPE) to frontline staff in hospitals and care homes, after it emerged that NHS bosses have asked doctors and nurses to work without protective full-length gowns when treating Covid-19 patients.

Chris Hopson, the chief executive of NHS Providers, said some trusts will run out of supplies on Saturday or Sunday, because the national stock of fully fluid-repellent gowns and coveralls was now exhausted.

On Friday, the business secretary, Alok Sharma, announced details of cash grants for research into vaccines and potential treatments, among them an antibody drug, which the government hopes could be given regularly to healthcare workers and other high-risk groups to provide protection over a few weeks or months.

A British Medical Association survey of more than 6,000 doctors across the country found a significant number do not have the protection needed to guard against Covid-19.

The BMA council chairman, Dr Chaand Nagpaul, said: “The government says that 1bn items will soon have been shipped, and while there have been signs of improvement, our research clearly shows that equipment is not reaching all doctors working on the frontline.

“Too many doctors and healthcare staff have already lost their lives. We cannot afford to risk losing any more. Just yesterday the health and social care secretary said he could not guarantee that hospitals would not run out this weekend,” Nagpaul added.

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At least 56 NHS workers have died from coronavirus. The actual number of health workers to have lost their lives is likely to be higher, as not all deaths will be in the public domain.