The Government announced prison officers would get a 1.7 per cent rise, while police will get a one per cent pay rise - plus a one per cent bonus for the year.
A report earlier this week claimed public sector workers were on average 10 per cent better off than those in the private sector.
The 2017/18 awards will be funded from existing departmental budgets.
Treasury minister Liz Truss said that hard working public sector workers deserved to be "fairly rewarded" and that special consideration was to be given to areas of the public sector where there were staff shortages.
The Royal College of Nursing has made it clear that industrial action is on the table if the government fail to scrap the pay cap.
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The Police Federation had requested a 2.8% increase in basic pay and the POA, whose general secretary Steve Gillan had stated that his members had suffered a £4,000 cut in pay since 2010, had wanted 5%.
"We are making sure that our policy is targeted to where there are specific issues, where we need to make sure we recruit more talent into the public sector, but also where we do need to make sure that we are holding on to those really valued people", she said.
And the hard-left union boss said he was ready to defy legislation requiring a strike to be approved by a ballot with a turnout of more than 50 per cent.
Theresa May admitted that there needs to be "more flexibility" so that employees are attracted to roles and stay in positions, meaning "world class" public services can be delivered.
Liberal Democrat leader Sir Vince Cable welcomed the move, saying: "It is good to see the Government finally recognise that the public sector pay cap is no longer sustainable. Our executive will be looking to co-ordinate action with other trade unions".
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This was rejected by Policing Minister Nick Hurd, who said the offer was affordable to forces.
"This below-inflation pay offer is pathetic", she said. Today's announcement means bills will continue to rise faster than their wages.
Mr Corbyn denounced the Government's announcement as an attempt to play "divide and rule" with public sector workers, and promised that Labour would ditch the cap across the board.
The prime minister's spokesperson said the government recognised the need for "flexibility" in pay for other public sector workers - including nurses and teachers - from next year, signalling an end to the 1% cap which was brought in in 2013. "We must be united in breaking the pay cap for all workers".
Unison general secretary Dave Prentis said: "We must commit to marching, demonstrating and lobbying - not just in Westminster, but in Belfast, Cardiff and Edinburgh too".
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