Long queues of traffic have formed across Lowestoft and Great Yarmouth despite assurances of there being "ample fuel stocks".
And as one service station was being restocked on Saturday morning, management urged people "not to panic".
While the entrance to the Gunton Service Station and Gulf Garage on Yarmouth Road in Lowestoft had been cordoned off, a tanker was on the forecourt delivering 37,000 litres of fuel from around 8am.
Nearby, dozens of cars were queuing to access the Tesco Petrol Filling Station on Leisure Way, Lowestoft with reports that early morning shoppers hoping to access the supermarket opposite were being caught up in the traffic.
Nationally, transport secretary Grant Shapps has urged drivers not to panic-buy amid chaotic scenes at stations across the country, as people continue to queue for fuel.
A similar message was being shared by Krishnapillai Prunthavan, manager at the Gunton Service Station and Gulf Garage in Lowestoft.
He said: "If people panic, we can't do anything.
"We now have a tanker delivering 37,000 litres, we are not closed and we will not be charging extra.
"But all we say is that the public need to help us as well - that is the only issue we have at the moment."
Staff admitted that it had been "madness" on Friday, with reports that customers were stocking up with £70 of fuel opposed to the normal £10 or £20.
One staff member added: "We are now being fully stocked and there is enough to go around for everyone if people consume at the same rate.
"Customers on Friday saw a 'fuel shortage' and everyone panicked.
"We had doctors and nurses coming in questioning how they would get to work."
There have been early morning reports that traffic is queued all around the roundabout near The Gateway Retail Park in south Lowestoft, as motorists queue to access the Morrisons petrol station on Tower Road.
In Kessingland, onlookers said traffic was "absolutely rammed" as motorists queued to access the Harvest Petrol Station on High Street.
One motorist queuing for fuel said: "It's chaos."
In Great Yarmouth, long queues of traffic had formed to access the Jet garage on Northgate Street, Yarmouth early on Saturday morning.
But the forecourt had soon been cordoned off with the garage closed around 9.20am.
The BP South Quay Station in Great Yarnouth is also reportedly out of diesel.
One motorist at the petrol pumps said: “It’s laughable.
"The whole world has gone nuts."
All pumps have also been closed at the BP garage on Caister Road, Great Yarmouth.
Onlookers described how cars could be seen pulling into one of the popular garages, and then making off straight away as drivers saw the pumps were closed.
Both Suffolk and Norfolk constabularies issued warnings on Friday, following reports of "drivers queuing at some petrol stations in Suffolk and Norfolk."
It added: "Keeping highways clear is essential for public services but particularly for emergency responders and hindering them could cause a public health risk."
Many drivers have also taken to social media to ask where best to go to refuel, while NHS workers and carers pleaded with people to “stop being selfish” as they feared being unable to get to work to look after Norfolk's most vulnerable.
A statement issued by Downing Street on Friday night said: “We have ample fuel stocks in this country and the public should be reassured there are no shortages.
“But like countries around the world, we are suffering from a temporary Covid related shortage of drivers needed to move supplies around the country.
“We’re looking at temporary measures to avoid any immediate problems, but any measures we introduce will be very strictly time-limited.
“We are moving to a high wage, high skilled economy and businesses will need to adapt with more investment in recruitment and training to provide long-term resilience.”
Other providers, including Esso and BP, have also been affected by challenges getting petrol deliveries across the country.
BP said that around 20 of its 1,200 forecourts in the UK were closed due to a lack of available fuel, and between 50 and 100 sites have been affected by the loss of at least one grade of fuel.
Esso owner ExxonMobil said a “small number” of Tesco refilling stations have also been impacted.
While some forecourts have issued limits on the amount individuals can put into their cars, other petrol stations have been forced to close.
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