Rishi Sunak’s first budget is not as generous as it seems and many Whitehall departments will still be worse off than they were before the spending squeeze began in 2010, according to Britain’s foremost economics thinktank.

The Institute for Fiscal Studies said the chancellor made the budget sound more substantial than it was, while relying on previously announced spending plans.

Paul Johnson, director of the IFS, said Sunak delivered a timely and well-targeted government response to the coronavirus but warned voter “expectations may be disappointed” from the promised increase in public spending.

In an assessment published a day after the coordinated response to the coronavirus outbreak from the Treasury and the Bank of England, the IFS said much of the longer-term spending rise designed to level up Britain was from previously announced measures for the NHS, schools, defence and overseas aid. “There is relatively little here for other departments,” Johnson added.

In an indication that a decade of austerity has had lasting effects, the IFS said spending per person for most public services will remain well below 2010 levels, despite Sunak’s expansionary budget.

Outside of the Department of Health and Social Care, which has had a protected budget, spending per head will still be about 14% lower than it was before the past decade of cuts began.

The thinktank said the loss of EU funds spent in Britain would mean spending per person of about 19% lower. With health and social care included, spending per head returns to 2010 levels in 2025.

Johnson said austerity was over in some respects, but that a decade of cuts to Whitehall departments had taken its toll. “If austerity is a process and a direction, then it’s over. If it’s spending above where we were in 2010, it’s with us for a very long time. But my sense is austerity is a direction rather than a level,” he added.

Although broadly praising the chancellor’s response to Covid-19, the head of the IFS said many self-employed workers would not get the support they might need and groups who may not be entitled to benefits could quickly face hardship.

“Sunak will certainly want to monitor the effectiveness of the package and be ready to come back with more if necessary,” he added.

The IFS said the government’s plans for a spending spree on transport projects and other public works was “genuinely very big”, although cautioned that the scale of the increase meant it would be a significant challenge to ensure the money was well spent.

The thinktank said Britain was more vulnerable to changes in interest rates, inflation and growth as the government pumps up borrowing levels and adds to the national debt. Sunak said at the budget he would balance day-to-day public spending with tax receipts by 2023, under rules set by his predecessor, Sajid Javid, with £12bn of headroom to spare.

However, the forecasts were drawn up by the Office for Budget Responsibility, the government’s independent tax and spending watchdog, before it could take full account of the coronavirus outbreak. The IFS warned that a downgrade in UK growth of just 0.3% a year over three years would eliminate all of Sunak’s headroom.

Johnson said: “This doesn’t look consistent with George Osborne’s mantra that the government should fix the roof while the sun is shining.”

Analysis of the budget by the Resolution Foundation thinktank said the economic hit from weaker growth over the next five years, despite extra spending by the government, will be about £300 per household this year, rising to £575 per year by the middle of the parliament.

“The budget does almost nothing to offset the considerable welfare cuts put in place by George Osborne in 2015,” said the thinktank.

Households with incomes just above the bottom 10th “will eventually be £2,900 a year worse off, on average, thanks to benefit and tax changes announced since 2015. With £900 of that yet to come as a result of welfare policies still being rolled out.”

It added: “These cuts mean the incomes of the poorest families have actually fallen over the past two years, and there is a risk that child poverty will reach record highs by the time of the 2024 election.”