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".
Cumbria has Haverigg prison in the south of the county.
Today the cabinet agreed to give prison officers a 1.7% rise while police will get a 1% pay rise plus a 1% bonus for the year, paid for from existing departmental budgets.
The jump in retail price inflation to 2.9 per cent last month has come at a hard, sensitive time.
"The cap must now be lifted across the board so all public sector workers are given the pay rise they deserve".
The federation had asked for a 2.8% increase to basic pay, while the Prison Officers Association had called for a 5% increase. The cap offer for the police and prison officers remains below the rate of inflation.
He said there had been a "genuine and evidence based" request for a 2.8 per cent rise.
Frances O'Grady, TUC general secretary, labeled the below inflation pay offer "pathetic".
Mr Serwotka said PCS members had suffered a 10% pay cut because of the cap, rising to 20% by 2020.
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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.
Four unions tabled motions to this week's Trades Union Congress in Brighton calling for some kind of nationally coordinated action, which were then included in a composite motion.
Leaders of unions representing millions of workers said they will continue campaigning for wage rises.
"In the first six years of Conservative rule, public sector pay rose by just 4.4%, yet the cost of living soared by 22%, and to rub salt into those wounds, the pay of top bosses rose by a third in one year alone".
"Make no mistake, our members across the public services are angry after seven years of pay pinching by the Government".
"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".
Steve White, chairman of the Police Federation of England and Wales, said the announcement was a "step in the right direction" but did not go far enough.
The Prime Minister's spokesman said the government would continue to deploy a "balanced approach to public spending" but recognised the need to address recruitment and retention issues in certain parts of the public sector.
The Treasury confirmed the police and prison officer rises and the move follows weeks of speculation the freeze may be lifted in response to growing anger about morale in the public sector.