The government has reassured people that there “isn’t a shortage of food” because of the coronavirus pandemic.
He said: “There isn’t a shortage of food, the challenge that we’ve had is getting food to shelves in time when people have been purchasing more.”
Supermarkets have stepped up their efforts to stop panic buying in recent days, restricting purchases across a wide range of products.
Stores have moved to reassure people that enough stock is being delivered every night, urging shoppers to purchase goods as they normally would.
But long queues have been reported up and down the country, with many people turning up before supermarkets even open.
There have also been reports of people pushing two trolleys around shops.
Facing questions from MPs on Thursday, Mr Eustice outlined the steps the government is taking to help deliveries reach stores.
He said one thing ministers are looking at is changing competition law to allow retailers and haulage companies to work together.
“We have taken steps including setting aside delivery curfews so that lorries can run around the clock, relaxing driver hours to ensure the deliveries can take place more frequently, and we are in discussions with other government colleagues in MHCLG [the Ministry of Housing, Communities and Local Government] around other support that we would deliver locally to get food to those who are self-isolating.”
Labour’s shadow environment secretary Luke Pollard said millions were “already in food poverty”, adding: “This is now an immediate family emergency for many of those.”
He asked: “With food banks running low on food, many volunteers of food banks over the age of 70 and soon needing to self-isolate, what steps is he taking to assist those in genuine hunger today?”
The environment secretary replied: “I’ve been in regular, daily calls with the food supply sector that included discussions around food banks and we are in dialogue with supermarkets to ensure we can make sure they get access to the supplies that they need.”
Mr Eustice added that the government was working on “specific proposals” to help the “most vulnerable”.
Mr Pollard called on the government to make sure that “every supermarket, not just the Co-Op, are still contributing to food banks”.
He said: “We won’t get through this crisis unless there’s government intervention to support those people and ensure that we have those food supply chains remaining open.”
Mr Eustice replied: “We must take action to set aside any obstacles to making the food supply chain operate in a way that will ensure people have food.
“On the issue of food banks, as I said, we are in discussions with supermarkets about this. We have also had discussions with them around competition law and will take whatever action is necessary to ensure they can jointly plan their approach to the matters.
“For the most vulnerable, we are working on proposals which my colleagues in the MHCLG will be announcing shortly.”