Justin King blamed the plunge in the value of the pound since Brexit for creating a "profound change" for food retailers.
Mr King said supermarkets would find it hard to calm price hikes while dealing with increased costs.
He told BBC Newsnight: "Something of around 40% to 50% of what we buy in the shops is sourced abroad in a currency other than the pound, and with the current rates of exchange we could expect that to be about 10% more expensive in a year's time. And if that's about half of what we buy, that means something of the order of 5% inflation."
The view was supported by the director-general of the Food and Drink Federation, Ian Wright, who told the BBC prices could increase next year by between 5% and 8%.