Senior Tories have urged Theresa May to end the benefits freeze in order to avoid electoral defeat.
Five former cabinet ministers are calling for benefits to be raised in line with inflation which would cost the Treasury £1.4 billion.
They were frozen in 2015 by George Osborne as part of a set of his austerity agenda and the policy is not due to change until 2020.
The Resolution Foundation says low-income households will be left more than £200 worse off next year, if the benefits freeze continues.
Experts say the cut to the welfare budget is one of the main reasons Universal Credit has pushed so many into poverty because it has meant cuts to the money they receive coupled with the built-in delay.
In the recent budget Chancellor Philip Hammond bowed to calls from charities, politicians and the Mirror by ploughing £1bn into the reform.
But pressure is continuing to grow on May to truly end austerity – after she made the pledge in her conference speech.
And Tories are worried that they will be punished at the ballot box if they fail to listen to people’s concerns.
According to the Times the Tory chairwoman of the Treasury select committee Nicky Morgan, five other Tory chairmen of select committees, the former work and pensions secretary Iain Duncan Smith and the former universities minister Lord Willetts also back the move.
The government has had to fend off a Tory revolt over benefits because of the problems with universal credit.
Mrs Morgan said that the chancellor should “look again” at the freeze – especially since the public sector pay cap has been lifted.
She said: “We always have to be wary as a party of being seen to know the cost of everything and the value of nothing.”
Former Brexit secretary David Davis said the “blanket freeze” was “in contradiction to the basic Tory notion of having a robust safety net and an effective ladder out of poverty”.
Ms Greening, the former education secretary, said: “The problem with a continued benefits freeze is it does not sit alongside recognition by ministers on public sector pay caps being lifted because of the need to keep pace with inflation.
“The system has to protect the most vulnerable.”
Mr Duncan Smith, the architect of universal credit, said that he would be “very happy” if the freeze were scrapped.
He said the extra money for universal credit was not enough.
“It was a step in the right direction but there will need to be more,” he said.
Tory MP Heidi Allen has been a strong critic of universal credit including organising the pre-budget revolt on the policy.
She told the Times: “The benefit freeze has gone on for too long; it does not make logical or moral sense to say that everybody else’s cost of living is increasing but people on benefits — often in work — that their cost of living isn’t increasing.”
A government spokesman said: “Tackling poverty is one of our fundamental goals and with this government’s changes there are now one million fewer people living in absolute poverty compared with 2010, including 300,000 fewer children.
“We know the best route out of poverty is through work, and universal credit is supporting people into work faster and helping them stay in work longer. Last week we announced that 2.4 million households would be £630 better off a year as a result of raising the work allowance.
“Since 2010 we’ve seen 1,000 people move into work each and every day and the increase to the national living wage has given the lowest earners a significant pay rise.”