The seven-year public sector pay cap is to be scrapped from next year, with ministers given “flexibility” to breach the long-standing limit of 1% on rises.
The announcement came as Downing Street unveiled a 1.7% hike for prison officers and improvements totalling 2% in police pay for 2017/18.
The end of the ceiling on public sector rises came after massive pressure from unions and Labour.
Next week a notice of motion will be raised by Sunderland councillors recognising public sector pay has fallen by 21% since 2010 in real terms and that employees have seen a crippling reduction in their standard of living.
It said the council wants to see and immediate end to the pay restraint and the Government to fund National Joint Council pay claim.
Nationally, unions made clear in their initial responses that the Government’s latest move and pay offers fell well short of their aspirations.
Public sector unions attacked news of more pay for police and prison officers as “divisive and wrong”.
Leaders of unions representing millions of workers said they will continue campaigning for wage rises.
Rehana Azam, national officer of the GMB said: “We do not welcome this announcement, which is nothing but smoke and mirror politics that insults our public sector workers.
“Make no mistake, our members across the public services are angry after seven years of pay pinching by the Government.
“The idea that robbing Peter to pay Paul, raiding already-stretched departmental budgets, will solve this problem, shows Theresa May is living in a fantasy land, far removed from public opinion.
“It’s divisive and wrong to make an announcement that excludes the vital support staff in the police and prison services who are subject to the same pressures as their colleagues.
“How will police and prison services cope without the extra funding they need?”
Unison general secretary Dave Prentis said: “It’s a tiny step in the right direction but not nearly enough.
“For seven long years the Government’s harsh pay cap has been hurting public sector workers, their families and the services they provide.
“There must be no selective lifting of the cap. No one part of the public sector is any more deserving than the rest.
“With inflation on the rise, the cap must go for everyone and it must go now.”
Steve Gillan, the general secretary of the prison officers union the POA, said the pay rise is actually a pay cut in real terms and he will be seeking to take industrial action for more money for public sector workers.
“Inflation is running at 2.9%. Anything below that inflation rate is a pay cut for our members. And a majority of our members will actually get a massive pay rise of 1.3%.
“I don’t know what the rest of the public sector is going to get.
“I have made it clear that it is a pay cut. It is not acceptable. Our executive will be looking to co-ordinate action with other trade unions.”
TUC general secretary, Frances O’Grady, branded the increases for police and prison officers “pathetic”, on a day when the latest inflation figures showed prices rising by 2.9% annually.
The POA prison officers’ union said it was seeking industrial action over an offer which it said effectively amounted to a pay cut and would leave a majority of staff with rises of just 1.3%.
Meanwhile, police chiefs warned that the pay award would put financial pressure on forces’ already-stretched budgets and could impact on their ability to deliver services and avoid job cuts.
Chief Secretary to the Treasury, Liz Truss, said review bodies and departments were being given greater leeway to use pay to address “pinch points” within public sector staffing.
She said: “What we are making sure is that we look at it on a workforce-by-workforce basis because there are very different issues for teachers than for nurses and for police officers.”
Theresa May’s spokesman said cabinet ministers “agreed that public sector workers are among the most talented and hard-working people in our society.
“They, like everyone else, deserve to have fulfilling jobs that are properly rewarded.
“Government will continue to ensure that the overall package for public sector workers recognises the vital contribution they make and ensures we can deliver world-class public services, while also being affordable within the public finances and fair to taxpayers as a whole.”
Liberal Democrat leader, Sir Vince Cable, said: “It is good to see the Government finally recognise that the public sector pay cap is no longer sustainable.
“The cap must now be lifted across the board so all public sector workers are given the pay rise they deserve.”
Labour leader Jeremy Corbyn said: “Let me be clear today. The Labour party totally rejects the Tories’ attempt to divide and rule, to play one sector off against another. A Labour government will end the public sector pay cap and give all workers the pay rise they deserve and so desperately need.”