The Telegraph has learnt that supermarkets are calling on ministers to relax competition laws allowing rival stores to open on alternate days and share staff.
The proposals would see food retailers, including the "big four", come together to maintain supplies.
One suggestion by supermarkets is to introduce co-ordinated closures, where rival shops near to each other agree to open on alternate days, allowing them to restock more easily.
Bosses are also in talks about sharing staff to prevent sudden store closures if large numbers of workers fall ill or have to self-isolate.
The bigger shops, which have on-site cafés and restaurants, have also been closing them and redeploying staff on to the shop floor.
Because some of the measures would technically be a breach of competition laws, the Government would need to remove legal barriers to such arrangements.
The proposals are being discussed along with rationing systems.
An industry source said: "There is a real desire for businesses in this sector to all work together to ensure food and other essentials are getting out to those who need them. By sharing staff, it is hoped they will be able to mitigate any losses through sickness and self-isolation. Supermarkets are also in talks about having coordinated closures so that different stores will open on different days. This would mean customers at least have some outlets open at any one time."
One sign of collaboration in the normally fiercely competitive world of grocery retail is the rationing agreements that have been reached.
But there remains concern over the issue of getting fresh produce from the fields into the shops.
The problem is being exacerbated by the unavailability of seasonal pickers, many of whom travel from abroad.
George Eustice, Secretary of State for the Environment, Food and Rural Affairs, is in talks with the National Farmers' Union over ways of addressing the shortfall.
Yesterday, Tesco became the latest major retailer to introduce rationing, with customers limited to three items across all products. From today, it has also closed its meat, fish and deli counters, and salad bars.
According to Government sources, the main concern for the sector is securing enough staff in May, when the majority of labourers travel to the UK.
HOPS, one of the leading suppliers of labour to farmers, has called on students, job seekers and staff laid off from catering and hospitality jobs to apply.
Sarah Boparan, HOPS' operations director, said: "We urgently need a UK labour force who can help harvest crops to feed the nation. As the peak season for soft fruit picking gets under way, HOPS is calling on British workers to help support the industry in jobs that are usually filled by EU workers."
The Royal Horticultural Society has also urged Britons to begin planting their own salad plants in gardens and even on windowsills, in a bid to become more sustainable.
Meanwhile, the police remain on standby to deal with any potential civil disobedience over shortages.
A source said: "At the moment, incidents have been sporadic and isolated and it is hoped that people will remain sensible and proportionate, but clearly the police are there if needed."
Alexander Stafford, the Conservative MP for Rother Valley, has written to the Prime Minister urging him to introduce legislation to outlaw the reselling of essential items by stockpilers.
In his letter, he claimed that a "black market" had sprung up of people "hoarding" and later reselling goods.
"These black-market profiteers need to be stamped out and shown that their actions are not only hurting innocent people, but also go against everything that Britain stands for," he wrote.
"No one should be making a profit out of other people's misery."
Source: The Telegraph