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.
Currently, Mr Johnson has only committed to reopening schools from March 8.
The Conservative MPs said ministers must produce a cost-benefit analysis to justify any controls that remain in place after early March, 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.
However, the government has repeatedly been warned by experts 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.
After schools reopen, the PM suggested on-essential retail will reopen next, with hospitality to open after that.
By Easter, which this year falls on April 4, the Tory MPs 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 enough time will have elapsed to allow them to have developed some immunity.
“All restrictions remaining after March 8 should be proportionate to the ever-increasing number of people we have protected,” the letter states.
“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.
Listen to ITV News's Covid podcast: Coronavirus: What You Need to Know