Ministers have called on people to stop "panic-buying" petrol and return to their normal pattern of purchasing as pumps run dry in some forecourts.
The UK's biggest operator is the Motor Fuel Group. Other companies include EG - which also owns Asda - along with Esso, BP, Shell, Tesco, Sainsbury's and Morrisons.
EG and Asda introduced caps on spending per driver, limiting fuel purchases to £30 in order to support its supply.
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A "small number" of Tesco refilling stations have also been impacted, said Esso owner ExxonMobil, which runs the sites.
BP said around 20 of its 1,200 petrol forecourts were closed due to a lack of available fuel, with between 50 and 100 sites affected by the loss of at least one grade of fuel.
A statement by Shell, ExxonMobil and other industry bodies said the pressures on supply were the result of "temporary spikes in customer demand".
Morrisons said: "It is a rapidly moving situation and we are working hard with our suppliers to ensure we can continue to keep our pumps open and serve our customers"
And Sainsbury's said: "We’re experiencing high demand for fuel. We’re working closely with our supplier to maintain supply and all our sites continue to receive fuel."
Following reports last week that BP had warned the Government that it would not be able to fulfil all deliveries due to HGV driver shortages, motorists became concerned and rushed to the pumps.
This caused a panic and led to a spike in demand, which further exacerbated the supply worries.
Yes. There is no issue with the amount of fuel going through refineries. Oil giant ExxonMobil, which operates Esso forecourts and runs the UK's largest refinery, said it is operating as normal and has "strong supply" to distribution sites.
The problem is getting it to the pumps and reacting to the latest surge in demand. The rising demand led the Petrol Retailers Association to warn that as many as two-thirds of its membership of nearly 5,500 independent outlets were out of fuel on Sunday.
Forecourt owners will be hoping the initial rush to the pumps will soon ease and supply can get back to manageable levels.
Operators have suggested that drivers can only stock up on a limited amount of fuel.
This should allow the shortage to subside more quickly than the supply problems seen at supermarkets at the start of the pandemic.
The Government has said competition laws will be scrapped temporarily, so companies can better liaise to deal with any shortages.
Reports had also suggested that drivers from the Army could be drafted to help with deliveries, although this was swiftly rebuffed by the Environment Secretary George Eustice.
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