Senior backbencher Steve Baker said he wants the prime minister to “let us reclaim our lives, once and for all”.
Health Secretary Matt Hancock said a roadmap out of the current restrictions would be outlined on 22 February.
The call comes as the government said it met its target to offer a vaccine to the 15 million most vulnerable people across the UK.
Over the weekend, 63 Tory MPs wrote to Mr Johnson, calling for easing to begin in March and for analysis to be released justifying any measures staying in place.
Mr Baker, who is the deputy chair of the lockdown-sceptic Covid Research Group of Tory MPs leading the call, said schools should return on 8 March, hospitality should re-open by Easter and all other elements should be back to normal by 1 May – when all people in the top nine priority groups have been offered a vaccine.
Steve Baker said in The Telegraph: “Now that the risk from Covid is rapidly diminishing as we roll out the vaccine to each of the top nine groups, we must focus on how we open up society in the short run.”
He also called for a new Public Health Act to ensure proper scrutiny for introducing lockdowns, telling BBC Radio 4’s Today programme it would “force the government to prove the proportionality of the measures it leaves in place”.
Mr Baker wrote: “We cannot live in a society where lockdowns are perpetually on the table, in fear that a minister might, without notice, impose restrictions that cost people their jobs, their livelihoods, their ability to date, to marry, to visit family at home and abroad, or to invest in their futures.
“As the prime minister said, let us reclaim our lives, once and for all. This can be a moment of unity – for our country and the Conservative Party – as we look ahead with confidence, hope and optimism to a much brighter future.”
Another senior Tory backbencher, Robert Halfon, said the PM needed to “provide some kind of optimism to the public” over lockdown easing, but warned against people relaxing too soon.
The chair of the Education Select Committee told BBC Radio 4’s Westminster Hour: “I understand where [the Covid Recovery Group] are coming from and my heart has a lot of sympathy.
“I just don’t want a repetition of what went on last year where we thought we were over the worst and then we’re suddenly back in tiers of lockdown.”
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