He joins charities and Tory MPs calling on the Chancellor to produce a fresh package of support after inflation hit a 40-year high. Cabinet wrangling is continuing over using a windfall tax on oil and gas producers - which have benefited from high global prices - to fund measures to help people with bills.
Mr Sunak appeared to acknowledge the need for further support for the poorest on Wednesday night as he said: "right now, we have a collective responsibility to help the most vulnerable in our society".
But he wants to avoid further straining public finances - battered in the pandemic - or introducing stimulus measures which fuel inflation.
Confederation of British Industry director general Tony Danker told BBC Radio 4 yesterday: "You have to help the hardest hit now. Helping people with heating and eating bills will not fuel inflation.
"You need to stimulate business investment now - that's not going to overheat the economy.
"It's going to make sure any downturn in our fortunes is short and shallow because growth is coming soon."
Inflation hit nine per cent in April, but analysts suggested the rate for the poorest, who spend a higher proportion of their income on food and energy, was above 10 per cent.
Petrol and diesel prices have climbed to new highs.
Labour says a windfall tax could fund a VAT cut on energy bills and an increase in the warm home discount for those on a low income.
The option is being considered by ministers, but the oil and gas industry warned that unpredictable taxes could deter investment and hit jobs.
Policing Minister Kit Malthouse told Times Radio: "We are intrinsically opposed to that kind of taxation." Measures being considered include increasing the warm home discount or bringing forward a 1p cut in income tax by a year to April 2023. Senior Tory MP Sir Bernard Jenkin said a £13.5billion support package was needed to address the cost-of-living crisis.
He said: "A summer package to rescue the most vulnerable households is needed to avoid real financial distress and personal anguish and to support the most vulnerable, or we are creating possibly a worse recession than is already expected."