Rachel Reeves will plough £2bn into affordable housing in a bid to “sweeten the pill” of the spending cuts being announced at this week’s spring statement.

The chancellor made the surprise announcement of the new cash – a down payment on the June spending review – as the Treasury bids to demonstrate that it remains focused on investment, rather than cuts. It will fund 18,000 affordable and social homes, part of the target to build 1.5m homes over the course of the parliament.

It comes as the governor of the Bank of England, Andrew Bailey, warned Britain faced “strong headwinds” to rebooting economic growth.

One Whitehall source said Reeves’ speech on Wednesday would go to significant lengths to remind MPs and voters of the significant spending and borrowing that the government had already undertaken, including spending on the NHS, free breakfast clubs, defence and housing.

Reeves will announce one of the tightest budget buffers on record, using the cuts to meet her fiscal rules and rebuild the government’s headroom after the Office for Budget Responsibility was expected to put the government about £5bn in the red.

The chancellor has told ministers she intends to restore headroom – the emergency spending fund available – as a way to demonstrate fiscal credibility, but the margin will be tight. At the October budget, Reeves has £9.9bn in headroom – less than half the average of £26bn over the past 15 years and the third smallest on record.

“Jeremy Hunt’s lowest was £6.6bn. She wants to get the finances back into black but there’s a judgment about how she does that and £10bn was a reasonable buffer to have last time. But she doesn’t have the same number of levers available to her as last time because this isn’t a budget,” a Treasury source said.

The prime minister, Keir Starmer, also attempted to dampen down growing unease over spending cuts in an interview on Monday, saying there were no plans to “alter the basics” of public spending.

“We are going to look across and one of the areas that we will be looking at is, can we run the government more efficiently? Can we take some money out of government?” he told BBC Radio 5Live.

The chancellor and the deputy prime minister, Angela Rayner, will announce the housing funding on Tuesday and herald it as the “biggest boost to social and affordable housing in a generation”.

One Whitehall source said the social housing announcement and the £600m in investment on construction skills announced over the weekend were attempts to “sweeten the pill” ahead of Wednesday by bringing forward plans from the spending review.

The £2bn will effectively bridge the gap between the current affordable homes spending due to expire in 2026 and the next funding settlement which will come in the spending review in June when a successor programme is expected to be announced.

The Treasury said it would mean the green light for thousands of new affordable homes to start construction by March 2027 and complete by the end of the parliament.

Rayner said it would “help us to build thousands more affordable homes to buy and rent and get working people and families into secure homes and on to the housing ladder”.

On Wednesday, the chancellor will say that the key planks of her approach will be maintaining economic stability, investment and reforming the state. Her spending cuts will have the theme of reform – the bulk of which will come from the painful £5bn in welfare cuts via changes to personal independence payments.

Another £2bn will come from changes to Whitehall’s administrative costs, expected to mean significantly more than the 10,000 job cuts suggested by ministers. Departments are also being asked to look at consultant spend and buildings costs.

There is also £1bn more to be raised via spending more money on tax collection, in plans Reeves will announce on Wednesday.

The Treasury will repurpose £2bn cuts to foreign aid to defence spending, which can be counted as capital investment and thus exempt from the fiscal rules –freeing up further cash in the spring statement.

Sources close to Reeves say she will vehemently contest the idea that the cuts are equal to George Osborne’s programme of austerity. “Scrapping NHS England is not austerity – it was created under austerity – but we have decided we need reform, we need to spend money better,” a Whitehall source said.

“Welfare – agree or disagree – is not simply about saving money, it’s about helping people back into work. Bringing technology into public services is not just about reducing head counts, it’s about making public services work.”

Treasury sources say there will be no other major headline-making cuts aimed at specific targets – and that the rest of the money to restore headroom will come from cuts to departmental budgets.

The specific areas that the cuts will hit are unlikely to become clear until departments get the full spending settlements at the spending review in June but departments have been asked to model cuts of up to 11%.

Sources close to Reeves and the education secretary, Bridget Phillipson, have denied cuts to free school meals are in their sights as part of plans to save £500m from education budgets.

“It’s no secret that there are some tough choices coming down the track – but if people don’t think Bridget is going to fight tooth and nail to protect programmes that support the most disadvantaged children, they don’t know Bridget very well. Any suggestions those things are being ‘offered up’ is complete rubbish,” a departmental source said.

In a speech on Monday evening at Leicester University, the governor of the Bank of England said he believed rekindling economic growth could be boosted by the adoption of artificial intelligence (AI) but there were challenges to overcome.

“We face a necessary challenge to raise the potential growth rate of the economy. There are strong headwinds. The combination of technology and trade remains an essential route to increasing productivity,” Bailey said.

Comparing the current moment to the UK’s role in the Industrial Revolution, he said the country now had an ageing population alongside barriers to free trade, as Donald Trump imposes tariffs on America’s allies and enemies alike.

Bailey said overcoming the roadblocks to growth would involve countries working together to tackle trade imbalances, as well as supporting workers to transition to the new jobs of the future. “We must also invest in new skills in the labour force – in our human capital,” he said.