Public sector pay was frozen for two years in 2010.
Ministers will now get "flexibility" to breach the longstanding 1% limit.
Martin Plummer, chairman of the county's police federation, said the move - announced by the Government today - was a step in the right direction.
Officers who work in correctional facitilies will receive an average 1.7% pay rise, while and police officers will receive additional pay totalling 2% for 2017/18.
"We've seen years of brutal austerity and vicious attacks on public services, overseen by an uncaring government whose pay policies are causing real hardship", he said.
"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".
"We need to strike a balance to be fair to public sector workers, recruiting the best people, and make sure we hold onto them".
News reports published late on Sunday said ministers were expected to accept recommendations for bigger pay rises this week, paving the way for similar increases for other government employees in future.
While there was very little support for talk of calling illegal strikes, legal action could be on the horizon.
On Tuesday or Wednesday (ministers making up minds) a strong signal will be sent that the 1% public sector pay cap is dead. Consumer price inflation is set to rise above 3 per cent in coming months and the...
He told a fringe event at the TUC conference today: "I have made it clear that it is a pay cut". It is not acceptable.
He said: "Police officers do not join the service to make huge amounts of money, they do it out of a sense of duty and this year in particular have been tested to the max".
White and the Federation which had called for a 2.8% increase to basic pay said, "We were not greedy in what we asked for", while the Prison Officer's Association had requested a 5% rise.
How much will it cost?
Downing Street announced on Tuesday that it would approve pay raises for police and prison officers in excess of the 1% public sector pay rise cap.
However, with other public sector workers having to wait longer for any increases, unions now meeting this week for their annual congress have warned industrial action could follow as a "last resort".
But there are other savings that need to be taken into account, for example, some have argued that raising pay in the NHS would stop staff leaving and reduce absence, so reducing the use of more expensive agency staff and saving money.
The 1 per cent cap has been in place since 2013, and the coalition had imposed a freeze before that.
Labour's shadow justice minister Richard Burgon refused five times to say if Jeremy Corbyn's party would condemn an illegal general strike in a auto crash interview this morning.
He added that police forces were "sitting on" at least £1.5bn in reserves.
Steve Gillan, the general secretary of the prison officers' union the POA, said: "Inflation is running at 2.9 per cent".
"Public sector workers have suffered seven long years of real pay cuts, and are thousands of pounds worse off".
Leaders of unions representing millions of workers said they will continue campaigning for wage rises.
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.
He said: "A pay cut is a pay cut".
The pay awards would come from existing Home Office and justice ministry budgets, the Government confirmed. Our message is simple: scrap the cap.
"There must be no selective lifting of the cap".