Rachel Reeves said she is “under no illusions” about the scale of the public spending challenge she will face if she becomes chancellor, as she declined to rule out real-term cuts to some departments.

The shadow chancellor said she has to be “honest that we’re not going to be able to turn things around straight away”, but said the Labour Party would keep its promises on education and health spending and would hope to secure more revenue through economic growth.

Ms Reeves acknowledged that “public services need more money” but a spending review, which would set departmental budgets, is not something she can do from opposition.

The Office for Budget Responsibility has said the current Government plans “imply no real growth in public spending per person over the next five years”, while the independent Institute for Fiscal Studies accused both the Conservatives and Labour of a “conspiracy of silence” about public spending after the election.

On BBC’s Sunday with Laura Kuenssberg, Ms Reeves was asked to confirm whether there would be real-terms cuts to some government spending.

She replied: “It is clear that the inheritance that a Labour government would have if we do win the next election will be the worst since the Second World War.

“And I have to be honest that we’re not going to be able to turn things around straight away. But we will get to work on all of that.”

She confirmed that plans for school breakfast clubs and measures to reduce NHS waiting lists would still go ahead, even though Chancellor Jeremy Hunt has already implemented the measures to tax non-doms which would have paid for them and instead put the money towards a cut in national insurance.

“I do know that public services need more money – that’s why we will make that initial injection,” she said.

And she said Labour’s plans for a national wealth fund to bring in private investment in low-carbon projects would boost growth and increase tax revenue for the state.

She said Labour measures to tax private equity executives and impose VAT and business rates on private schools would also generate cash for public services.

Ms Reeves said she would be scouring government documents to identify additional funding streams and stressed “everything in our manifesto will be fully costed and fully funded”.

But she said she is “under no illusions about the scale of the inheritance and I do need to be honest that it’s going to take a while to turn around the challenges that we see”.

Labour has called in business chiefs and economists to advise on how to use its national wealth fund to leverage private investment.

Former Bank of England governor Mark Carney, Aviva chief executive Amanda Blanc and Barclays boss CS Venkatakrishnan are on the taskforce.

Labour has pledged to invest £7.3 billion in the fund to support the growth of a zero-carbon economy, with each £1 of public money required to bring in £3 of private sector investment.

Ms Reeves said: “The idea is to leverage in private sector investment alongside a government endowment to invest in some of the jobs and industries of the future, from carbon capture and storage to green hydrogen and green steel, floating offshore wind and so much more – areas where we can be a world leader, where we can bring good jobs paying a decent wage to Britain, start to bring people’s energy bills down and also boost our economic security by boosting our domestic energy security.

I'm really pleased that what businesses can see is that Labour have a serious plan

“And I’m really pleased that what businesses can see is that Labour have a serious plan. We are determined to get in that private sector investment and they want to work with me and the Labour Party on how we can get that up and running if we are fortunate enough to win the next election.”

Ms Reeves also used the BBC interview to highlight how she wants to tackle waste – including by ensuring croissants left over from breakfast meetings go to her staff.

“I don’t like waste of expenditure – I don’t like any waste. When you go to these events and there’s all these pastries left out at the end, we ask whether we can take them back to the office and share them with colleagues – living out my values in practice, no waste under a Rachel Reeves chancellorship.”

The Tories said Labour’s spending commitments on school breakfast clubs and NHS improvements were unfunded following Mr Hunt’s Budget, which deprived Ms Reeves of the non-dom funding.

Chief Secretary to the Treasury Laura Trott said: “For five days Labour have been unable to say how they’re going to pay for their unfunded spending commitments. That’s because they don’t have a plan to pay for it and that means higher taxes, taking us back to square one.”