Tesco’s UK boss has warned that food price inflation could prove highly toxic for shoppers and lethal for those on a tight budget.

Matt Davies said: “Everybody should be very, very clear how damaging food inflation is to the economy, to retail businesses and manufacturing businesses and how lethal it could be for millions of people struggling to live from week to week.”

He spoke out after Tesco became embroiled in a public spat with one of its main suppliers, Unilever, after the maker of brands including Marmite and Persil demanded an across the board 10% rise in prices in light of the devaluation of the pound after the the EU referendum.

The two companies reached agreement on Friday after it emerged that Tesco was running low on stocks of more than 20 popular Unilever brands because the supplier halted deliveries when the supermarket would not agree to its price demand.

Davies, who was speaking at the Big Debate conference organised by grocery industry body IGD, said it was clear there were inflationary forces in the UK after the Brexit vote but would not say whether they would feed through to price rises on supermarket shelves.

“Our role is to do everything we can do to prevent food inflation which is not good for business and highly toxic for consumers,” said Davies, who joined Tesco from car parts and bicycle retailer Halfords 18 months ago.

Inflation rose to its highest level in two years in September, according to official figures released on Tuesday, but the Office for National Statistics said there was no “explicit evidence” that it was having a significant impact on consumer prices. However, some analysts are warning that shop prices will start to rise next year as insurance contracts taken out against currency fluctuations come to an end and supermarkets struggle to offset rising import costs.

Mike Coupe, the boss of Sainsbury’s, told the IGD event it was not clear whether there would be food price inflation.

“We’ve seen significant devaluation of the pound but equally we’ve got commodity price movements the other way,” he said.

“If you look at fuel as an example, when the pound devalued, [international] oil prices also fell. Pump prices went up by a couple pence, but by no means as far you might have expected in the circumstances.

“We operate in a world market where supply and demand will also adjust itself and products will be sourced from different areas of the world to mitigate [cost increases] to some extent. Having said that, there are inflationary pressures on the industry and it would be wrong to shy away from that.”

He and Davies spoke as industry data revealed the lowest rate of grocery deflation in almost two years.

Analysis firm Kantar Worldpanel said grocery prices fell by an average 0.8% in the three months to 9 October, the smallest drop since December 2014. A month ago, Kantar said grocery prices fell by 1.1% in the three months to 11 September.

Bruno Monteyne, a retail analyst at Bernstein Research, said: “[The figures] suggest we are starting to see the pound weakness feeding through to less deflation.” His firm calculates that over the latest four-week period deflation is likely to be significantly less than 0.8%.

But Tom Wharram, who also works for Bernstein, said that while shoppers might not welcome the prospect of lower deflation, or potentially inflation, the situation would not necessarily be bad for retailers. “Historically, retailers have been good at passing on input costs to customers and we think they will do that again if food inflation comes back. The benefit on margin will be limited but it will help their top-line growth and investor sentiment,” he said.