Supermarkets regard cutting prices as “very important”, according to a former boss of Asda, after the Prime Minister warned retailers about pricing “responsibly and fairly”.

Andy Clarke, who served as Asda’s chief executive officer between 2010 and 2016, said the big chains were “heavily focused” on competitive pricing as the industry hit back over suggestions it has looked to maintain profit margins by passing on inflated costs to customers.

“I’m sure if you are one of the chief executives of the supermarkets, whether that is the top four or five, or the discounters, pricing and bringing pricing down for families is still very important to them,” Mr Clarke told BBC Radio 4’s Today programme.

The British Retail Consortium (BRC), the trade body representing the sector, said there had been a “regular stream of price cuts” by supermarkets despite experiencing “extremely tight” profit margins.

It comes after Prime Minister Rishi Sunak said he wanted to see the burdens of the weekly shopping bill “easing” and that household weekly shopping bills had “gone up far too much in the past few months”.

Let’s make sure that they cut their prices as fast as they put them up on the way up

Chancellor Jeremy Hunt has confirmed that ministers are talking with the food industry about “potential measures to ease the pressure on consumers” after the Bank of England said some retailers might be “rebuilding” their profit margins in the face of stubborn inflation by hiking prices.

Harriett Baldwin, the Conservative chairwoman of the Treasury Committee, voiced her own concern on Friday that declines in wholesale prices were “not necessarily passed on very fast to consumers”, who are in the grip of a cost-of-living crisis.

“We do have a competitive grocery sector in this country, we do have a lot of supermarkets, there is a lot of competition,” she told Today.

“Let’s make sure that they cut their prices as fast as they put them up on the way up.”

The Consumer Prices Index (CPI) inflation, one of the main measures of price growth, remained at 8.7% in May, surprising experts who had forecast that it would fall.

Increases in food prices did slow between April and May, according to the Office for National Statistics (ONS), having reached a 45-year high in March.

But consumer groups have continued to warn about the rising price of basic goods, with the ONS reporting that the food inflation rate stood as 18.4% last month.

Helen Dickinson, chief executive at the BRC, said: “Supermarket margins remain extremely tight as retailers try to absorb the worst of the rising costs and protect their customers.

“(The) CPI announcement showed the second consecutive month of falling food inflation, even as headline inflation remained unmoved.

“Despite some prices continuing to rise, we are seeing a regular stream of price cuts being reported by the media as retailers do their best to ease the cost-of-living pressures faced by their customers.”

Ms Dickinson said ministers could make changes that would help ensure “inflation rates continue their downward trend”.

She added: “They should review those incoming policies that will push up costs for businesses, including a deposit return scheme in England and an increase to business rates.

“Most importantly, Government should extend the timelines for the £2 billion-a-year reformed packaging levy (Extended Producer Responsibility), to ensure a fit-for-purpose scheme that improves recycling rates without adding to the current inflationary pressures.”

Consumer campaign group Which? said the Prime Minister had been “right to the focus on supermarkets” when addressing the economy’s inflation problem.

Ele Clark, the organisation’s retail editor, said: “The Government must prioritise consumers by getting supermarkets to urgently commit to stocking essential budget ranges in all their stores, particularly in areas where people are most in need, as well as make pricing much clearer so shoppers can compare prices and find the best value products.”

Labour leader Sir Keir Starmer said he wanted to see supermarket prices “as low as they can be in the circumstances”.

He told broadcasters during a visit to RAF Brize Norton in Oxfordshire that he did not think that capping the prices of grocery staples was “realistic”, with the idea reportedly having been considered by Downing Street.

Sir Keir instead argued for farmers to be given support with their energy costs and for attention to be paid to fixing the “blockages and the red tape” associated with the UK’s Brexit deal, which he said was “slowing food down, making it more expensive”.

“There are things that can be done and need to be done in a crisis like this,” he added.