It comes as Chancellor Rishi Sunak makes the case for pay restraint to reflect a fall in private sector earnings this year.
It is thought that frontline NHS workers will be exempt from the pay rise restrictions given their work during the Covid-19 outbreak.
Mike Clancy, general secretary at civil servants' union Prospect, said: "After a decade of pay austerity in the public sector which has seen pay increases lag behind inflation and the private sector, a further pay freeze across the public sector will be seen as an insult and have a devastating impact".
It came as the Office for National Statistics yesterday confirmed that public sector debt hit £2.08 trillion in October, with Government borrowing in the first seven months of the financial year rising to an estimated £215bn.
However teachers, police, members of the armed forces as well as NHS managers will all be affected.
How much money will it save?
Commenting on fresh reports that this will involve a public sector pay freeze exempting NHS workers, Anneliese Dodds said: "Workers on the Covid front line have kept our country going through this pandemic". Our key workers are still feeling the effect of ten years of Tory austerity, pay freezes and squeezes...
Alternatively, it said that an annual 1% pay cap would save £11.7 billion over the period - or £7.7 billion if it did not apply to healthcare workers.
But there were complaints that many workers missed out, and unions plan to campaign against the new pay freeze. At the same time, there is a need to control public spending and reduce the structural deficit which the pandemic is likely to have opened up. "Some businesses are folding under the strain, public finances have been decimated, while the public sector has escaped relatively unscathed", said Robert Colvile, director of the Centre for Policy Studies.
However, launching the spending review in July, Mr Sunak warned of the need for "restraint" in future public sector pay settlements. "If they want fairness across the economy they should heed our call for an independent pay-review body and stop public-sector pay being a political football".
In July, nearly 900,000 public sector workers were given an above-inflation pay rise - including doctors and teachers - due to their "vital contribution" during the pandemic.
What has the reaction been?
"On the very day we discover the government is planning a pay freeze for millions of workers, GMB is gearing up to lodge a judicial review against the government decision to swindle public sector workers of their pensions should they leave their employment due to redundancy".
Responding to the CPS report, the union Unite said the analysis was "insulting to those public sector workers that have underpinned the fabric of society during this continuing pandemic".
Unison general secretary Dave Prentis said: "Reports of pay restraint for all but frontline NHS staff would be a cruel body blow to other health, care and public service employees working tirelessly to get us through the pandemic". The cap was lifted in 2017.
Public sector pay in England and Wales was frozen in 2010 and then capped at one per cent from 2013.