Lord Rose said that food prices will stay higher for some time due to the high cost of raw materials.
The Conservative peer warned that many families are going to suffer because of the cost of living crisis.
The Bank of England expects price inflation to go up.
The Business Secretary said that inflation would not be long term.
Families in the UK are having a hard time with rising energy, fuel and food costs.
The chairman of Asda said on the Sunday Morning programme that he was worried that food prices were going to stay high for a long time.
The war in Ukraine and the resurgence of Covid in China are some of the pressures on prices.
The war in Ukraine has pushed up oil and gas prices even more.
With the price hikes being passed on to consumers, this is ramping up raw materials costs for manufacturers and retailers.
Chicken feed is going up, and all the other costs are going up.
Pasta is made from durum wheat, which has gone up in price, so that is an inevitable cost increase.
Chicken could become more expensive than beef because of the war in Ukraine, according to the Co-op's chief executive.
Some of the prices at the fast food chain went up in April.
Lord Rose said retailers would do what they could to shield customers from raw materials cost increases, but that they were not immune from cost increases of their own.
He said supermarkets have staff, electricity, fuel, insurance and transport costs.
If you bake biscuits or cakes, the energy used goes into the cost of the raw material that you have to pass on to consumers.
There is a danger of long-term effects on the economy from high inflation, such as a wage spiral and Stagflation, where prices and wages go up but the economy doesn't grow.
The government has a difficult road to navigate because they are both evil, according to Lord Rose.
He said that most of their customers were very worried about the cost of living and how they were going to make ends meet.
There is an issue with cost of living increases, but we don't know how long that will last.
He asked, "Who can say how long any inflation will last?"
The government was dealing with it by creating jobs.
The government's energy security strategy, which includes new nuclear and offshore wind power generation, will not cause high inflation for a long time.
Labour has called for a windfall tax on oil and gas companies.
Labour leader Sir Keir Starmer told Sky News that they are not talking about taxing the profits. The profits they didn't expect to make.
We would use that to reduce energy bills by up to 600 for those who need it.
David Lammy, Labour's shadow foreign secretary, told the BBC that families with cost of living pressures should not have to pay more in National Insurance. The rise will help recover from Covid and fund social care in England, according to the government.
He said it was the wrong time for people to face a National Insurance rise.
Sir Ed said inflation would be high for at least a year or two.
Millions of people are worried about the cost of living.
This week, as most people received their pay packet, they finally see the reality of the cost of living crisis - a hike in National Insurance, soaring bills and no support from the government.