The Prime Minister said 350,000 people in the UK have received the first dose of the Covid-19 vaccine, as his chief medical officer suggested the jab gives room for optimism amid a “terrible” moment in the pandemic.

Boris Johnson revealed the number of people who had already received the initial injection of the Pfizer/BioNtech vaccine during a Downing Street press conference on Saturday.

Appearing alongside him, Professor Chris Whitty, England’s chief medical officer, said the spread of a new variant of coronavirus was another “terrible” moment in the pandemic, but not “the worst” because of medical treatments and the vaccine rollout.

He said: “Is it the worst moment? Well I’m afraid there have been so many terrible moments in this epidemic this is another one.

“But I have to say in my own view this is not the worst moment in the epidemic and the reason for that is although this virus is more transmissible and we must do everything we can, which is what the Prime Minister has announced, to keep it as constrained as possible, keep it down as much as possible, so it does not spread.”

Prof Whitty added: “We do have medical countermeasures, we have a vaccine already being rolled out as the Prime Minister said and therefore there is a prospect, relatively in the medium-term future, where things could be quite a lot better.”

He acknowledged that the new strain would “make things a lot worse”, but there were “optimistic things” if the vaccine works against it – something that was a “working assumption”.

In a statement issued earlier on Saturday, Prof Whitty said there was “no current evidence to suggest the new strain causes a higher mortality rate or that it affects vaccines and treatments”, but work was under way to confirm this.

During the press conference, he said if coronavirus case numbers could be brought down across the country “that will give us a chance to get the vaccine out and protect the most vulnerable people so that if it does then escape what we have is the barrier of the vaccine to help protect them.”

His comments came after former health secretary Jeremy Hunt warned stocks of coronavirus vaccine could run out at the end of January unless new ones such as the Oxford jab are approved.

Mr Hunt told the BBC’s Today programme on Saturday that if the Oxford-AstraZeneca vaccine was approved soon it would make a “massive difference” because current stocks of the Pfizer jab will run out at the end of January.

Mr Hunt’s comments come amid reports the Oxford vaccine could be approved before the new year, with the Daily Telegraph reporting senior Whitehall sources believe the Medicines and Healthcare products Regulatory Agency (MHRA) will authorise it on December 28 or 29.

Mr Hunt, who is also chairman of the Health Select Committee, said that if the Oxford-AstraZenca vaccine is approved by regulators before the end of the year it will ensure that the roll-out of the vaccination programme can be maintained.

A Government spokesman said millions more doses of the Pfizer/BioNTech vaccine will be available in the coming weeks.

Pfizer said that shipments of the vaccine will be arriving in the UK before March next year, with deliveries on track and progressing according to its agreed schedule.

The Royal College of GPs chairman Professor Martin Marshall also said the rollout of the coronavirus vaccination programme in care homes will be sped up if the Oxford-AstraZeneca vaccine is approved by regulators.

But the MHRA said its review of the Oxford vaccine was still ongoing.

About 200 GP-led vaccination clinics were expected to be up and running by the end of the week, with more to follow.

To date, 800,000 doses of the Pfizer vaccine are known to be in the country, which is enough for 400,000 people.

Overall, the UK has ordered 40 million doses – enough to vaccinate 20 million people.

Meanwhile, the Moderna Covid-19 vaccine has been given authorisation for use in the US by the country’s Food and Drug Administration (FDA).

The move marks the world’s first clearance for Moderna’s shots, and the vaccine is very similar to one from Pfizer and Germany’s BioNTech jab which is already being rolled out.