Richard Walker, Managing Director of Iceland told ITV News: "We have spoken to Government about this.
"My hands are still tied with these archaic Sunday trading laws.
"This is a moment of national crisis and we need our shops open".
The supermarket boss also wants the Government to change advice to shoppers.
Richard Walker said: "If you are fit, if you don't fall within the highly vulnerable category, if you adhere to social distancing guidelines - you should go out to stores because that will free up slots for the most vulnerable customers."
ITV News understands that 400,000 of those vulnerable people lack support from family or neighbours to help.
Fazilet Hadi of Disability Rights UK is blind, she's getting help to shop.
She told ITV News that others are becoming desperate: "I think things are getting quite grim.
"I think they are getting through what food they did have and I think they definitely need help.
"The worry is some of these people wont be the people that speak out, they'll be the people who are silent".
The Department for Environment, Food and Rural Affairs (Defra) has said it is not considering considering extending Sunday trading hours.
In a statement, the department said it had taken a number of other actions during the crisis: "We are working quickly to support people who do not fall into the category of being clinically vulnerable, but still need help getting essential food supplies.
"We are speaking to food retailers, delivery organisations and volunteer groups to help prioritise those individuals to access essential food.
"Wherever possible, people should continue to rely on friends, family and wider community support.
"We have also introduced a range of measures to keep food supply flowing and support home deliveries, such as issuing guidance to local authorities to allow extended delivery hours to supermarkets so that shelves can be filled up more quickly, and implementing extensions to drivers’ hours."