Police and prison officers will this year receive a pay rise that busts through the public sector pay cap, but it will still be an effective cut because living costs are rising faster.

Both groups will be given a rise equating to more than the one per cent cap on increases that has limited public sector workers during years of austerity.

But the increases offered by ministers will still be lower than the rate of inflation, which at 2.9 per cent has risen faster than economists expected - meaning the offer is a real terms reduction in their spending power.

The offer was met with an angry reaction from Frances O’Grady, General Secretary of the TUC, which is in the middle of its annual conference in Brighton.

Theresa May's Cabinet this morning agreed a one per cent rise for police in 2017/18, plus a "non consolidated" additional one per cent - giving an effective two per cent rise this year.

Prison officers will be given a 1.7 per cent rise, with the increase funded from within existing budgets in both cases.

A Downing Street spokesman said: "The Cabinet agreed that our public sector workers are among our most talented and hardworking people in our society. They like everyone else deserve to have fulfilling jobs that our fairly rewarded.

"The Government takes a balanced approach to public spending, dealing with our debts to keep our economy strong, while also making sure we invest in our public services.

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"The Government will continue to ensure that the overall package for public sector workers recognises the vital contribution they make, and ensures that we can deliver world class public services, while also being affordable within the public finances and fair to tax-payers as a whole."

While the spokesman said there would still be a need for "pay discipline" in future, he added: "The Government recognises that in some parts of the public sector, particularly in areas of skills shortage, more flexibility may be required to deliver world class public services, including in return for public sector productivity."

The Cabinet agreed that the detail of next year's 2018/19 pay remits for specific occupations, will be discussed and agreed as part of the budget process and be set out in due course

It emerged this morning that inflation rose unexpectedly to 2.9 per cent in August, as the slump in sterling since the Brexit vote continued to have a powerful impact on domestic UK prices.

The reading was up from 2.6 per cent in July and outstripped expectations of City of London analysts of a 2.8 per cent increase.

The Government's pay announcement is unlikely to quell discontent in many parts of the public sector, including the NHS, with the Royal College of Nursing threatening strike action if a fair rise is not delivered for its members.

Ms O’Grady said from Brighton: "This below-inflation pay offer is pathetic.

"Public sector workers have suffered seven long years of real pay cuts, and are thousands of pounds worse off. Today’s announcement means bills will continue to rise faster than their wages.

"If Ministers think a derisory rise like this will deal with the staffing crisis in our public services, they are sorely mistaken."

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Public sector pay restraint was first implemented in 2010 by then-chancellor George Osborne as a freeze, and then a one per cent cap later on.

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."

Labour’s Paul Blomfield has said that Labour would join union members on the picket line if there was no rise in public sector pay, but rejected the use of illegal strike action.

Speaking on the Daily Politics on BBC Two, he said: "All parts of the public sector deserve a pay rise… we have a review body structure which will make the recommendations that are right and we think there should be justice for all of those workers."

Liberal Democrat Leader Vince Cable called for the cap to now be lifted across the board.

He added: "Nurses, teachers and other public sector workers are set to be hundreds of pounds worse off in real terms as a result of rising inflation.