“We want to do more to help keep costs down for families,” the spokesperson added.
The proposals, first reported by the Financial Times, external, come after the Scottish National Party (SNP) pledged to introduce a similar policy in Scotland last month. However, its price cap would not be voluntary.
The BRC dismissed the policy as “1970s style price controls” while one retailer described the idea as “crazy” and the act of a “desperate” government.
Another told the BBC: “Ultimately what [the government] should do is stop all the other tax burdens and the prices will come down.”
The rate of food price rises is currently 3.7% – while the overall rate of inflation stood at 3.3% in March.
Some industry groups have warned the rate of food price rises could hit nearly 10% by the end of the year.
One retailer said government policies, including rises in the national living wage and employers’ national insurance contributions, had increased costs in food supply chains.
Others say price rises are being caused by a surge in fertiliser and animal feed prices since the US-Israel war with Iran effectively blocked their transport through the key Strait of Hormuz waterway.
Helen Dickinson, BRC chief executive, said there was already “fierce competition between supermarkets”, which had driven down prices.
“The challenge facing retailers is a combination of higher energy and commodity costs resulting from the Middle East conflict, and the soaring cost of the government’s domestic policies,” she added.