After his spring statement was criticized for failing to provide enough help for families facing the biggest drop in living standards since records began in 1956, Rishi Sunak hinted at further support for families in the fall.

The chancellor said the government would “certainly” do everything in its power to help pay gas and electricity bills if energy regulator Ofgem raises the household price cap in the autumn.

“When we get there and see what happens, you know, of course, as I said, we’ll look at the situation and see what needs to be done,” he told BBC Radio 4’s today program.

Sunak used Wednesday’s announcement to offer some relief to households, raising the threshold at which state insurance must be paid by £3,000, cutting fuel taxes by 5p a litre a year and proposing a 1p cut in income tax in 2024. “Yesterday we announced the tax package that will provide people with significant help in the coming months and years,” he told today.

But amid runaway inflation and rising energy bills, the chancellor is now under increasing pressure to roll out a larger family relief package in the autumn.

The home energy price cap has jumped by £693 to £1,971 in April. Estimates released on Wednesday by the Office for Budget Responsibility, Britain’s financial watchdog, show that from October 1, households could earn more than £2,800 a year. Ofgem reviews the cap twice a year.

After Sunak’s spring statement, a quick YouGov poll found that 69% thought he had not doing enough Help people increase the cost of living.

Over the next financial year, people’s living standards (disposable household income adjusted for inflation) will fall by 2.2%, the largest drop on record, the OBR said.

It concluded that Sunak’s tax cuts would only offset a quarter of the tax increases announced in last October’s budget. The OBR added that the overall tax burden will rise from 33% of GDP in 2019 to 36.3% in 2026, the highest level since the 1940s.

Wednesday’s tax cuts pale in comparison to previously announced tax hikes, which include a rise in NICs’ rates, a looming corporate tax hike and a freeze on the income tax threshold.

The Treasury is facing major headwinds after spending nearly £400bn to tackle the Covid-19 pandemic and now a surge in wholesale gas prices globally that has pushed up energy bills, petrol pump prices and inflation. “We are all grappling with global inflation and a reaction to Putin’s aggression,” Sunak said.

Official forecasts predict inflation could peak at nearly 9% by the end of the year, far exceeding public sector wages.

While Sunak wants to make room for a pre-election income tax cut, he conceded on Wednesday: “We should prepare for a deterioration in public finances, perhaps significantly.”

Sunak’s failure to escalate benefit payments in line with inflation means an additional 600,000 people will be pushed into poverty, the Joseph Rowntree Foundation think tank has warned.

Labour said the tax cuts in its spring statement were nowhere near enough to offset the cost of living crisis.

“Ordinary families, people with disabilities and pensioners are facing very difficult choices,” Shadow Chancellor Rachel Reeves said. “Mums skip meals to keep their kids off. Families struggling to buy new school shoes and uniforms for their kids. Older people hesitant to install heating because of cost concerns.”

But with prices continuing to fluctuate in the wholesale gas market, Sunak said it was worth waiting until closer to the next Ofgem announcement to intervene.

“We’re going to have to get to this point and we’re going to see where we are,” he said on Thursday. “If there is a major problem, the government will always do what it can to help. I have proven that time and time again over the past few years.”