Nurses, care workers, ambulance staff and police are all among those who have been left stranded as pumps ran dry due to a shortage of HGV delivery drivers.
Chaos at the forecourt could drag on for up to a month even if panic buying stops, according to industry insiders.
According to industry insiders, disruptions at petrol stations could take several weeks to stabilize due to the time required to replenish supplies.
Sources claimed that BP would continue to address the problem throughout October.
Police, nurses, ambulance personnel, and care workers are just a few of the people who were left without power after pumps went dry from a shortage in HGV delivery drivers.
Unions urged No10 not to stop panic-buying by allowing key workers to fill up at petrol stations as soon as they can.
Meanwhile, Boris Johnson said the crisis at the petrol pumps was “stabilising” and urged Brits to “go about your business” as normal.
The Prime Minister admitted it was “frustrating and infuriating” for families but the situation was “starting to improve”.
Despite the assurance industry sources told The Times that the disruption could rumble on for weeks even if panic buying fades because of the time it takes to restock petrol stations.
The outlet was told by a source that BP would continue to address the problems through the next month.
Due to a shortage of lorry drivers, petrol stations across the country have faced fuel shortages. This has caused chaos for motorists.
Ministers struggled to deal with the crisis and had to call in troops to drive petrol tankers.
Earlier, Transport Secretary Grant Shapps resorted to pleading with drivers to stop bringing “water bottles” to petrol stations.
Mr Johnson told reporters: “I want to say, first of all, how much I sympathise with people who’ve been worried about their journeys, worried about whether they’ll be able to use their cars in the normal way, to see their loved ones or whatever it is, and I know how frustrating, infuriating it must have been to worry about shortage of petrol or fuel.
“We now are starting to see the situation improve; we’re hearing from (the) industry that supplies are coming back on to the forecourt in the normal way.
“I would really just urge everybody to go about their business in the normal way and fill up in the normal way when you need it.
“We want to ensure that we are prepared for Christmas and beyond. Not just supply for petrol stations, but also all parts of the supply chain.”
The PM tried to claim that shortages of drivers had been inflated and said there had been a surge in demand due to a “The shortfall is somewhat misleading.