Cabinet minister George Eustice has suggested that struggling families use value brands to save money, but ruled out a windfall levy on oil and gas firms by arguing that fossil fuel giants pay enough tax already.

The environment secretary said prices would continue to rise at the supermarket and will “undoubtedly put pressure” on household budgets amid the cost of living crisis.

Asked what hard-pressed families could do, he told Sky News: “Generally what people find is going for some of the value brands, rather than own-branded products they can actually contain and manage their household budget.”

Labour deputy leader Angela Rayner responded by tweeting: “Let them eat value cake? The Tories haven’t got a clue.”

Mr Eustice claimed that “the price of food in and of itself doesn’t necessary cause poverty”, but acknowledged that the combination of “very sharp rise in energy costs” and other price hikes were placing a huge burden on people.

However, the minister insisted that oil and gas companies already paid enough tax as he rejected growing calls for a levy on their windfall profits. “We need to see them investing,” said Mr Eustice.

BP announced on Tuesday that its underlying quarterly profits more than doubled to £5bn thanks to the rocketing cost of crude. But Mr Eustice said the company already makes a “significant contribution”.

It comes as Boris Johnson’s government comes under growing pressure to provide more support to ease the pressure on household finances.

On Tuesday the prime minister pointed to the £200 “rebate” loan set out by the chancellor Rishi Sunak earlier this year – but admitted it isn’t going to be enough immediately to help cover everybody”.

Mr Eustice conceded the £200 rebate was simply a “loan” – but insisted it will help people pay bills this year.

Defending the chancellor over the failure to provide more help with bills, he said: “We can’t just keep borrowing huge amounts more money. … There’s a real risk inflation would rise further still.”

The environment secretary was also asked about the case of 77-year-old ITV viewer called Elsie – who travels on buses all day to reduce her bills.

“In that particular case, I really would advise the woman would be to go to the local authority and try to get some support from that Household Support Fund – it’s what it’s there for,” Mr Eustice said.

The minister conceded the £200 rebate for energy bills was simply a “loan” – but insisted it will help people pay bills this year.

Asked if BP and other oil and gas firms pay enough tax, he told Sky News: “For now, yes. And that’s why we’ve chosen not to do it [a windfall tax].”

He told Sky News the situation would be kept under review but “for now we judge that, yes, it is right that these oil companies pay more and they already do pay more – the headline rate of income tax or corporation tax is already 10 per cent higher.”

The minister added: “Nothing’s ever obviously ruled out, the tax system is kept under constant review, we have two key fiscal events a year.”