Lockdown-sceptic Tories have piled pressure on Boris Johnson, calling on him to commit to a timetable for lifting coronavirus restrictions with a complete end to controls by the end of April.

In a letter to the Prime Minister, the leaders of the Covid Recovery Group (CRG) said the “tremendous pace” of the vaccination rollout meant restrictions in England should begin easing from early March.

They said ministers must produce a cost-benefit analysis to justify any controls that remain in place after that date, with a “road-map” stating when they would be removed.

The letter was organised by the CRG chair and deputy chair, Mark Harper and Steve Baker, and was said to have the backing of 63 Conservative MPs in all.

In other coronavirus developments:

– Health Secretary Matt Hancock wrote in the Mail on Sunday that he “danced a little jig” over the joy the coronavirus vaccine can bring.

– NHS England has begun sending out letters to 1.2 million of the next group of clinically vulnerable and the 65 to 69 year-olds inviting them to book an appointment as the next phase of the vaccine rollout begins.

– Former Prime Minister Tony Blair reiterated his calls for a global coronavirus vaccine passport scheme, writing in the Mail on Sunday: “We have the technology which allows us to do this securely and effectively. The need is obvious. The world is moving in this direction. We should plan for an agreed ‘passport’ now. The arguments against it really don’t add up.”

It comes as the ministers said they are confident they will meet their target of getting an offer of a vaccine to all 15 million people in the UK in their four priority groups – including all over 70s – by Monday’s deadline.

During a visit to a vaccine manufacturing facility in Teesside on Saturday, Mr Johnson said he was “optimistic” he could announce plans for a “cautious” easing of the rules when he sets out his “road-map” out of lockdown on February 22.

However he said ministers would have to look at the data “very, very hard” before taking any decisions as they did not want to to forced into a “reverse ferret” if the disease started to spread again.

In contrast, in their letter, the CRG said the Government’s “national priority” of re-opening schools in England by March 8 “must” be achieved.

By Easter, they said pubs, restaurants and other hospitality venues should be able to open in a way that is Covid-secure but still allows them to operate “in a commercially viable manner”.

And by the end of April – when all the Government’s top nine priority groups, including all over 50s, should have been offered a vaccine, they say there will be “no justification” for any legislative restrictions to remain.

“Covid is a serious disease and we must control it. However, just like Covid, lockdowns and restrictions cause immense social and health damage and have a huge impact on people’s livelihoods,” the letter said.

“The vaccine gives us immunity from Covid but it must also give us permanent immunity from Covid-related lockdowns and restrictions.”

The letter points out that by March 8 the Government’s top four priority groups -which account for 88% of deaths and 55% of hospitalisations – will have had their first dose of the vaccine at least three weeks earlier allowing time for protection to kick in.

“All restrictions remaining after March 8 should be proportionate to the ever-increasing number of people we have protected,” it says.

“The burden is on ministers to demonstrate the evidence of effectiveness and proportionality with a cost-benefit analysis for each restriction, and a roadmap for when they will be removed.”

Downing Street refused to be drawn on reports suggesting that restrictions on meeting friends in a park could be among the first to be lifted once schools are back.

The Sunday Times and The Mail on Sunday reported that all schoolchildren in England will be back in the classroom on March 8, although The Sunday Telegraph said the return of secondary schools could be delayed by a week.

While it is thought restrictions on outdoor recreation are likely to be among the first to be eased once schools are back, Government sources stressed ministers will only start to seek the data which will determine the pace of any relaxation this week.

“Whilst there is some reason for cautious optimism, we remain in a difficult situation, with the pressures on the NHS still very significant. We have to go at the pace that the latest data and evidence allows,” one source said.

“Our biggest priority remains schools, and we will set out our plan for reopening them, and gradually reopening our economy and society on February 22.”

Elsewhere, Professor Sarah Gilbert, who led the team behind the Oxford/AstraZeneca vaccine, said it was “really heartening” to see the NHS getting the vaccine out to so many people.

However she warned that lessons from earlier disease outbreaks had still not been learned.

“Yes, this particular virus came out of nowhere. But we have also known for a long time that a disease X, as the WHO (World Health Organisation) termed it, was going to appear at some point and start spreading,” she told The Observer.

“We had been warned. But again we weren’t ready.”