The compromise over George Osborne’s controversial measure will hit many of the same people already losing their tax credits

The chancellor, George Osborne, is expected to fund the softening of the blow of controversial tax credits reductions by taking away housing benefit from many of the same people who will lose out.

Osborne’s tax credit changes were defeated in the House of Lords last month, with many in his own party worried they would punish working families unfairly.

The transitional arrangements will be set out in the five-year spending review, which will include further cuts at the Home Office for Theresa May – expected to lead to another round of reductions in frontline policing. The chancellor will also be forced to admit that deficit reduction forecasts for this year have proved over-optimistic and his hope of reaching a £10bn surplus at the end of the parliament is unlikely to be fulfilled.

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But Osborne insisted on Sunday that the only route to long-term economic security – and ultimately national security – lay in cutting the deficit.

The spending review, alongside new economic forecasts, will see cuts of up to 20% over the parliament across a range of departments. The decisions on Wednesday will lead to fundamental changes to the shape of public services, according to Paul Johnson, the director of the Institute for Fiscal Studies.

The chancellor is also likely to press ahead with a manifesto commitment to cut welfare spending by £12bn, but he will slow the process of withdrawing tax credits from this April by offering transitional support through the parliament.

Many of the long-term cuts to the income of the working poor will be introduced through reductions to universal credit – which supersedes tax credits – that the chancellor forced through the Commons in a low-profile welfare committee vote last week.

Last month, Osborne was forced to backtrack on his plans to cut tax credits after a backbench rebellion and defeat in the Lords.

Cuts to local government grants will be offset for councils by the ability to increase their council tax by up to 2%. This funding, called the social care precept, must be used to fund local social care services. There are also likely to be cuts to the schools budget.

Alan Milburn, the chair of the social mobility commission, urged Osborne to think how targeted spending on teachers’ pay in deprived areas could reduce the educational attainment gap and boost long-term growth.

Research by the commission suggests that “if the UK [were] able to close the education attainment gap between the most advantaged children and everyone else by two-thirds by 2035, the UK’s long-run growth rate would ultimately be 15% higher”.

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Trying to lower the temperature before Wednesday’s announcements, the chancellor told the BBC’s Andrew Marr show: “I’ve read all these reports in the newspapers that I’m at war with various members of the cabinet.

“I can tell you, the spending review has been agreed, all departments have settled – and all settled amicably – nothing has been imposed and indeed this spending review has gone more smoothly than than the two previous spending reviews I’ve done.”

Asked directly if there will be cuts to frontline police, Osborne said: “Of course, the police do an incredibly important and brave job on our behalf. Every public service has to make sure it is spending the public’s money [well] … and there are efficiencies that can be made in the police and how they buy their equipment, and how they operate their back offices.

“We made savings in the police budget in the last parliament and actually, the number of neighbourhood police officers went up.”

Questioned about how he was responding to the calls to row back on the cuts to tax credits, Osborne said: “I’ve said of course I’m prepared to listen to those who say can we ease the transition to this lower welfare, higher wage economy. But my central judgment [is this]: we need to make savings in welfare.

“I’ve always been someone who thought it’s not a weakness to listen to good arguments.”

But, suggesting his ultimate destination remained unchanged, he added: “I’m pretty confident we can deliver what we promised the British people we’d deliver at the general election, which is – yes – savings in welfare, savings in government … for a purpose, which is economic security: the security that enables jobs to be created and living standards to rise in this country.”

The shadow chancellor, John McDonnell, said Osborne’s economic and fiscal plans were in utter chaos months after he announced them.

“We all know he gave up a long time ago on his 2010 promise to eradicate the deficit by today, but now he can’t even stick to the deficit-reduction plans he announced as recently as July,”McDonnell said.

“Labour [was] the first to call on the chancellor to target a lower surplus as a way he could reverse his tax credit cuts and stick to his self-imposed fiscal straightjacket. Now it seems he is being forced to take our advice as his economic and fiscal plans are falling apart.

“Rather than engaging in a cynical Westminster game of smoke and mirrors in this week’s spending review, it’s time the chancellor acknowledges the challenges facing our country. He must reverse his tax credit cuts and fully protect frontline policing from any cuts.”