Urgent action is still needed to make it easier for vulnerable people to access supermarket delivery slots and other sources of supplies.
Consumer group Which? argued vulnerable people were at risk of going hungry because the current system is not working for those who need it the most.
It said people are still struggling to book supermarket delivery slots, unable to find the help they need locally, and in some cases find themselves forced to risk their health to get supplies.
Some vulnerable customers have told Which? that they are staying up into the early hours of the morning in an attempt to book supermarket delivery slots.
Sue Davies, head of consumer protection and food policy at Which?, said: "Based on the huge number of reports we’re seeing from vulnerable people struggling to get access to basic food and supplies, it’s clear that the current system is not working for those who need it the most."
One vulnerable couple, who are relying on a neighbour, described supermarket delivery slots to Which? as 'gold dust', while a housebound woman claimed she had been 'trapped with no deliveries for three of the past four weeks'.
Which? agreed that many supermarkets have gone to great lengths to increase their capacity, but it needed a more co-ordinated effort from government to improve access to deliveries.
It wants to see governments at national and local levels, the food industry and local charities to link, so that all options for providing food deliveries, from supermarkets to local shops and volunteers, are used fully.
There should also be a simpler process for people at highest risk to register for help to get the type of food supplies they need, Which? said.
Ian Hudspeth, chairman of the Community Wellbeing Board at the Local Government Association (LGA), said: "Councils are working hard to protect those most vulnerable to this virus and to support the Government scheme to deliver food and supplies to those in the shielded group.
“Councils are already showing leadership and establishing local arrangements to support vulnerable residents outside this group, who are struggling to access food and support due to their isolation or because of hardship."
Association of Convenience Stores chief executive James Lowman said: "We encourage anyone who is shielding, self-isolating or otherwise unable to leave their home to contact their local convenience store.
"Thousands of convenience stores have stepped up to ensure that vulnerable people get the essentials that they need, providing over 600,000 home deliveries a week, and enabling volunteers to collect and pay for goods on behalf of others."
A Government spokeswoman said: "We are determined to ensure the most vulnerable are supported during this pandemic.
"Working closely with councils, the NHS and the food industry, we have delivered over 900,000 parcels of food to clinically extremely vulnerable people through the shielding programme.
"For those who do not fall into the shielded group, there is other support available. Vulnerable people can refer themselves to the NHS Volunteer Responders programme by calling 0808 196 3646. Local councils may also be able to offer emergency support."
