The calls come as Scottish First Minister Nicola Sturgeon jumps ahead of the UK government to announce Scotland's plans to end lockdown.
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Ms Sturgeon stressed the strict measures were still "absolutely necessary, but said Scotland needs "to chart a way forward" ahead of releasing their guide to ending lockdown today.
The First Minister revealed students may be allowed back to school part-time, with social distancing still in place.
She told Heart Radio: "We might have kids going back to school for certain days a week.
"We may have to have children in a classroom so that we can have social distancing."
Ms Sturgeon's announcement will come only hours after the Government's Chief Medical Officer Chris Whitty admitted the UK might have social distancing measures in place until next year.
Discontent is growing among Conservative backbenchers who are calling for a clear, "safety-first" exit strategy from shutdown to protect the economy.
Treasurer of the 1922 Committee Sir Geoffrey Clifton-Brown is one of the leading voices in the demand for answers.
He told BBC Radio 4: "We need to start this discussion of how we get back to normality.
"Whatever we do needs to be done gradually, when the figures start to stabilise more in three to four weeks, hopefully we could begin to think about what's the next step."
He said it was essential to open up parts of the economy, to rescue them from being completely decimated by the lockdown.
"I see no reason why garden centres, DIY stores with proper social isolating couldn't begin to open.
"We have to think about the number of small businesses, who unless they get some form of business, may have to cease trading.
"We have to accept that at the moment a relatively small amount of the population has been exposed to the virus – we are going to expose more people to the virus
"We have to on behalf of the businesses of this country, begin to give them a little bit of hope.
"People have been cooped up home and some will be able to get quite difficult mental problems as a result of that.
Sir Geoffrey and other members of the 1922 Committee of Tory backbenchers called a private meeting yesterday where they unanimously expressed deep concern of the continual lockdown, according to The Times.
Boris Johnson has made it clear the UK will not leave lockdown unless several conditions are met – including a steady drop in new infections and deaths.
The Government has said they will not begin to talk about how the lockdown will end until these conditions are met, and the focus should be on people staying home.
Last night Professor Whitty said the nation was still weeks away from seeing a significant decline in numbers.
Professor Whitty said: "We are working with a disease we are going to be with globally for the foreseeable future."
"(There are) lots of options which ministers will have to consider."
They key to ending lockdown was to ease measures in way where no infected person is, on average, infecting more than one person.
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Northern Ireland First Minister Arlene Foster has said measures could be eased at a different pace than in other parts of the UK.
She said the criteria for easing restrictions "will be set down and agreed" by the Northern Ireland executive as well the UK Government.
She told Cool FM this could mean "different parts of the UK move (at) different times".
Sir Geoffrey said: "The nation is quite divided on this and it's up to the government, I think, to exercise leadership."
"Unless we do something fairly soon the economy is going to take a real hit."
Vice Chairman of the committee Sir Charles Walker said "There has got to be an economy to go back to.
"All MPs right now are dealing with dozens if not hundreds of local businesses that are fearing for their future.
"Building capacity within the NHS, reducing infection rates has to be the precursor to lifting the economic lockdown. If we don’t do this many good and strong businesses will not open their doors again.
"The consequences for millions of people will be potentially devastating."