Tesco chairman John Allan has warned it is “very likely” that prices will rise, following the devaluation of the pound after Brexit.

Allan said: “We are trying to defend our customers from unjustified price increases but that it is likely there will be some price increases going forward, I think is very likely.”

His comments follow that of Tesco UK boss Matt Davies, who told the IGD conference last week that the grocer would do “everything” it could to keep prices low, in the wake of its well-publicised battle with Unilever.

He told the IGD Big Debate: “We are very, very clear that as the number one food retailer in the UK that inflation is a bad, bad thing in food.

“We will do everything we can do on behalf of customers across the UK to make sure that inflation on food is kept to a minimum. That’s our focus.

“Everybody should be very clear how damaging inflation is to the economy, to retail business, to manufacturing business and how lethal it can be to millions of people who are struggling to live from week to week.”

But Allan said yesterday that it was almost certain that the decline in the value of sterling would push up the consumer price of the cost of imported food, and ingredients for products made in Britain.

He poured cold water on the suggestion that food prices could rise between 10% and 20%, saying it would be “much less” and that he believed inflation might “nudge up” 2% to 3%, with food prices contributing to that.

In an interview with the BBC, Allan declined to comment on the supermarket’s recent row with Unilever over raising the price of goods such as Marmite by 10%.

But he said: “We see our role as retailers not to prevent our suppliers from making legitimate cost increases where they think that’s necessary but certainly scrutinising those cost increases very hard.”

Allan also cautioned Prime Minister Theresa May on immigration controls, saying that the agricultural industry was “heavily dependent” on overseas workers, both seasonal and permanent.