A decision on a new date will likely be put to a Commons vote later this month, with a Tory rebellion already brewing.
Sir Charles Walker, vice chair of the powerful 1922 Committee of backbench Tory MPs, said the country should be ending the lockdown “sooner rather than later”.
He warned of the impact lockdown had on people’s mental health, likening people’s homes to the “dark satanic mills” of the Industrial Revolution.
He told BBC Radio 4’s World At One: “We have many young people chained to their small bedrooms and kitchens. So the new dark satanic mills are now people’s flats.
“Remember, most of the people making the decisions around this have very comfortable lifestyles. And those we’re asking to pay the highest price now are the youngest.”
Sir Charles said he had an “overwhelming sense of pessimism” that if the Government cannot lift restrictions at the height of summer then we are “almost certainly” looking at further restrictions into autumn and winter.
He said if we were to live with Covid-19, at times we would have to “tough it out” and added: “Existing isn’t living. We were told we were going to live with Covid-19 and it now looks like most of the remaining of this year, and certainly the first half of next year, will probably end up with some form of lockdown.”
Asked if he thought the easing of restrictions could be reversed he said: "Yes I do."
Conservative MP Damian Green suggested on BBC’s Westminster Hour on Sunday night that there should be a “break clause” after two or three weeks.
He said: “If there is a delay, I hope it’s only for a few weeks and I think if it is as long as a month then there should be a break clause after two or maybe three weeks, to say that if we can tell by then that the rise in cases is not lading to a sort of rise in the serious illness that sends people into hospital, then we can unlock earlier.”
Meanwhile fellow Tory MP Peter Bone said a delay to the lifting of restrictions should not happen "without really good reason" and that currently he "can’t see the evidence why we should be postponing our freedom".
He said if he is not convinced by the Prime Minister’s arguments then he will vote against it in parliament and there should only be restrictions "if there is a very clear danger to society".
Mr Johnson is expected to announce a delay because of the highly transmissible Delta variant and to allow more people to receive their second vaccine dose.
Health Minister Edward Argar said a delay of “four weeks or so” could ensure more people get the extra protection afforded by two doses of vaccine. He said the Government sees getting people double-vaccinated as “the key to being able to safely ease restrictions”.