More than 60 MPs on the Covid Recovery Group have backed a letter to Boris Johnson demanding he commits to a strict timetable for ending controls in England.
They said schools “must” return by March 8 as planned with pubs and restaurants reopening from Easter.
Mr Raab said the Prime Minister would be setting out his “roadmap” out of lockdown on February 22 as promised, but that any decisions would depend on the data.
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“We do need to be very careful how we proceed. We have made good progress. We don’t want to see that unravel because we go too far too quick,” he said.
“We are not making what feels to me like a slightly arbitrary commitment without reviewing the impact that measures have had on the transmission and the hospital admissions of the virus.
“I don’t think you can set though an arbitrary target and not be evidence-led, which is why the review point on February 22 is so important.”
Mr Raab said the Government was confident it was “on track” to meet its target of offering a vaccine to its top four priority groups in the UK – including all over-70s – by Monday.
He said they were still aiming to start reopening schools on March 8 – although he would not be drawn on whether they would all be able go back at the same time.
“We need to wait to evaluate the data carefully and allow those plans to be put in place,” he said.
“Because we are making progress I think we can be confident we will be able to start that process.”
He indicated that allowing people to socialise outdoors and the reopening of non-essential shops would also be early priorities as controls eased.
In their letter, the leaders of the Covid Recovery Group (CRG) said the “tremendous pace” of the vaccination rollout meant restrictions in England should begin easing from March 8.
They said ministers must produce a cost-benefit analysis to justify any controls that remain in place after that date, with a “roadmap” 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.
“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.”
It 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.”
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 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 be forced into a “reverse ferret” if the disease started to spread again.
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