Labour has called for an independent assessment of whether Rishi Sunak’s £21bn cost of living emergency package could cause inflation to rise even higher and a verdict on the fiscal impact of substantial borrowing.

Pat McFadden, shadow chief secretary to the Treasury, wrote to the Office for Budget Responsibility (OBR) to ask it to analyse the impact of the measures.

He said that, although the sums were “of the order of magnitude that would normally be announced within a budget”, the UK’s tax and spend watchdog should “provide authoritative and independent economic and fiscal projections”.

Pressure on the government to do more to help those facing spiralling fuel and food bills ramped up substantially last week, when the energy regulator, Ofgem, admitted that the cap on household energy bills looked likely to rise by a further £800 in autumn.

In response – some have suggested partly as a ruse to shore up support in the aftermath of the Sue Gray report into Partygate – the chancellor unveiled handouts worth £21bn.

He also U-turned to support a windfall tax on offshore oil and gas companies’ profits – a move that senior government figures and Tory MPs had discredited for months when Labour initially called for it.

The move was well received by most Tory MPs, and McFadden himself said Labour “welcomes these announcements”. But because the announcement came in a fairly poorly attended Commons statement the day before recess, the OBR did not examine the measures as closely as it would other major economic statements.

“With at least £10bn of new borrowing announced yesterday, there should have been an accompanying report on the fiscal impact of the measures taken by the chancellor,” McFadden said. “It is right that families get the support they need, and also right that the country knows how the chancellor is paying for this.

“Labour’s fiscal rules would ensure that the OBR had oversight of any package we introduce in response to a crisis such as this, ensuring that we get the best value for the public purse, and this is why we have written to them to seek their assessment.”

McFadden’s letter to the OBR’s chair, Richard Hughes, called for an assessment of the measures on public sector expenditure, receipts and net borrowing, as well as gross domestic product and investment.

Sunak argued that the support was targeted and designed to help “those who are paying the highest price for the high inflation we face”.

After his announcement, the Brexit opportunities minister, Jacob Rees-Mogg, admitted he “sees the concerns” of Tory MPs worried about the inflationary impact of substantial government spending, but said it was a “very difficult balancing act”.

The OBR and Treasury have been contacted for comment.