The chancellor has hinted that she may give public sector workers above-inflation pay rises this summer.

Rachel Reeves’ comments come after independent pay review bodies recommended an increase of 5.5% for teachers and some NHS workers.

In her first interview from No 11 Downing Street, she said: “I really value public service workers, in our schools, in our hospitals, in our police as well…

“There is a cost to not settling, a cost of further industrial action, and a cost in terms of the challenge we face recruiting.”

But Ms Reeves told Sunday with Laura Kuenssberg that “we will do it in a proper way and make sure the sums add up” – emphasising that her spending rules are “non-negotiable”.

The new chancellor promised a decision on public pay this month, saying “people won’t have long to wait”.

Speaking in an interview to be broadcast on Sunday morning, Ms Reeves also accused the Conservative Party of calling the election because “they weren’t willing to make tough decisions, and they just ran away”.

She said the decision about teachers’ pay had sat on the former education secretary’s desk, and that the Conservatives had allowed an unacceptable situation to build up in prisons.

The estimated cost of pay rises of 5.5% for teachers and certain NHS staff could reach £3bn, according to the Institute for Fiscal Studies (IFS). That would be significantly more than the 2.5-3% the Treasury had expected.

IFS director Paul Johnson said paying for such an increase would require the government to either increase borrowing or taxes, or cut spending elsewhere.

The most recent figures from the Office for National Statistics (ONS) put inflation at 2% in May and June – suggesting a pay offer above 2% would count as being above inflation.

But Mr Johnson told BBC Radio 4’s Today programme on Saturday that the 5.5% figure was “roughly what pay is rising by across the economy”.

Traditionally, governments follow the recommendations of the independent bodies – but ministers are not obliged to stick to their suggestions.

Recommendations for other sectors are yet to be received, but the chancellor does plan to announce the settlements before the end of July.

Ms Reeves also told the BBC that the government will carry out a landmark review of pensions as part of a “big bang for growth”.

“People who make sacrifices and save every month to put something aside for their retirement, they deserve better than the returns they’re getting on those savings today.”

The chancellor also wants to change industry rules so that billions of pounds sitting in pension funds can be used more easily to invest in UK companies to stimulate the economy.

She continued: “If we could unlock just 1% of the money in defined contribution schemes – and invest that in more productive assets [and] fast-growing British companies – that’d be £8bn to help finance growth and prosperity and wealth creation here in Britain.

“That’s why there’s an urgency here from this government, unlocking that investment for our economy and delivering for working people who make big sacrifices but at the moment are being let down by the pensions industry.”

The full interview will be broadcast on Sunday with Laura Kuenssberg at 09:00 BST on BBC One and iPlayer. Shadow chancellor Jeremy Hunt will also be on the programme.