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

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.

It comes amid warnings from scientists advising the Government that lifting restrictions too quickly risks another wave of the disease as big as the current one.

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

By Easter, they say 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 at all.

“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.

“This should be a moment of unity – for our country and our party – as we look ahead with confidence, hope and optimism for a much brighter future, as we reclaim our lives once and for all.”

The letter points out that by March 8 the Government’s top four priority groups – including the over 70s, accounting for 88% of deaths and 55% of hospitalisations – will have received the vaccine and will be protected.

“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.”

Among the restrictions about which they had “concerns” were those relating to outdoor sport and swimming pools, gyms, personal care businesses, care home visits, hotels, events industry businesses, and weddings.