Labour has offered to sing from the same hymn sheet as Government ministers on the vaccine rollout in order to give the public “confidence” in the newly approved jab.

Opposition leader Sir Keir Starmer said he was making the “extraordinary offer” to the Prime Minister because the vaccine project, which he described as one of the biggest logistical exercises since the Second World War, would require the “best of Britain”.

The comments come after the Labour leader asked Boris Johnson at Prime Minister’s Questions to share with him the Government’s communication plan for making the Pfizer jab, which was approved by the Medicines and Healthcare products Regulatory Agency (MHRA) on Wednesday, widely available.

We need the best of Britain, we need parties pulling together and I’m very happy to put my party behind that effort

Speaking to broadcasters in Westminster, Sir Keir said: “It is an extraordinary offer and it is one I’m making.

“I think it’s really important that as we roll out the vaccine that all of us, whatever our political party, work together to make sure that the rollout is swift, safe and fair and that people have confidence in it.

“So I’ve invited the Prime Minister to share with us their communications and then we will work together so that the public can see cross-party consensus on this because this rollout is one of the biggest logistical exercises since the Second World War.

“We need the best of Britain, we need parties pulling together and I’m very happy to put my party behind that effort.”

The former director of public prosecutions said the logistical issues around administering the vaccine, which has been produced jointly with BioNTech, had to be overcome because “care homes have suffered enough”.

Sir Simon Stevens, chief executive of NHS England, told a Downing Street press conference that most care home residents – who are at the top of the priority list – will need to wait for their Covid-19 injection because of difficulties in transporting the vaccine.

He told the briefing that the jab had to be stored at such low temperatures that it can only be moved a few times, while the packs of doses – with 975 doses per pack – cannot be easily split.

Sir Keir called on ministers to declare their plan for “rolling this out swiftly, safely and fairly” even with the “problems” surrounding its storage.

He said: “We know there are limited numbers to start with and that doesn’t cover all the groups that need the vaccine straight away, so we need to know who is going to be vaccinated next week, how’s that going to work?

“I think there’s a real problem with care homes and how we get the vaccine into care homes – logistical problems because the vaccine has to be kept at such low degrees and cold.

“But we’ve got to overcome that and we’ve got to pull together because people in care homes have suffered enough already.”

He reiterated his PMQs call for emergency legislation to be passed to tackle anti-vaccine misinformation.

“It’s really important that people have confidence in the vaccine, we all have to make the case that the vaccine is safe,” Sir Keir added.

“But I think we do need legislation to deal with those who are putting out bad and false information which in the end is going to cost lives, and we need emergency legislation I think to deal with that.”