The cost of raw materials will keep food prices high "for quite some time", Asda chairman Lord Rose has said.
Many families struggling with the cost of living crisis are "going to suffer", the Conservative peer warned - although he said he believed that retailers will try to keep costs down.
Speaking to the BBC Sunday Morning programme, the Asda chairman said he feared that food prices "are going to go higher, and they are going to stay high for quite some time".
Pressures on prices include the war in Ukraine and a resurgence of Covid in China, said Lord Rose.
Oil and gas prices were already rising rapidly before Russia's invasion of Ukraine, but the war has pushed prices up further.
In turn, this is ramping up raw materials costs for manufacturers and retailers - including for meats like chicken and staples such as pasta - with the price hikes being passed on to consumers.
"Chicken feed is going up, and all the other associated costs are going up," he said.
"I see no quick solution to this.
"Pasta is made from durum wheat, and durum wheat has gone up in price, so that's an inevitable cost increase."
Co-op chief executive Steve Murrells told the Sunday Times that chicken could become as expensive as beef due to the war in Ukraine.
Fast food chain Nando's, which specialises in chicken, said that some of its prices had gone up in April.
Lord Rose said retailers "will do what we can" to shield customers from raw materials cost increases, but added they were "not immune from cost increases ourselves" and would pass them on.
The Bank of England expects price inflation to hit 8% this spring.