Drivers are being urged by the Government to "buy fuel as normal" as the lorry driver shortage hits supplies across London and the south east.
BP said a "handful" of its filling stations are closed due to a lack of fuel available, while Esso owner ExxonMobil also said a "small number" of its Tesco Alliance petrol forecourts have been impacted.
A Government spokeswoman said: "There is no shortage of fuel in the UK, and people should continue to buy fuel as normal.
"We recognise the challenges facing industry and have already taken action to increase the supply of HGV drivers, including streamlining the process for new drivers and increasing the number of driving tests.
"We continue to closely monitor labour supply and work with sector leaders to understand how we can best ease particular pinch points."
Jim McMahon, Labour's shadow transport secretary, said it was a "rapidly worsening crisis" and accused the Government of "never investing in or valuing working-class jobs".
He went on: "Sticking plaster solutions are not going to solve it.
"Ministers must take decisive steps now to tackle the 90,000 driver shortfall."
BP told the Government in a meeting last Thursday that the company's ability to transport fuel from refineries to its network of forecourts was faltering.
BP's head of UK retail Hanna Hofer said it was important the Government understood the "urgency of the situation", which she described as "bad, very bad", according to a report by ITV News.
She added that BP had "two-thirds of normal forecourt stock levels required for smooth operations" and the level is "declining rapidly".
Meanwhile, an ExxonMobil spokesman said: "A small number of our 200 Tesco Alliance retail sites are impacted.
"We are working closely with all parties in our distribution network to optimise supplies and minimise any inconvenience to customers."
A Tesco spokeswoman said: "We have good availability of fuel, with deliveries arriving at our petrol filling stations across the UK every day."
The HGV sector has been struggling with recruitment in recent months with a combination of the Covid-19 pandemic and Brexit reducing the number of available drivers.
With test centres shut and many HGV drivers from the EU returning home during the pandemic, it has created a shortage of qualified drivers.
The issue has already hit supermarkets, with shelves half full and grocers forced to increase salaries and introduce signing on bonuses to fill gaps.
It has spread to waste collection services, with some councils cancelling bin collections as drivers have taken more lucrative jobs elsewhere.
Calls from Morrisons and Ocado for the Government to add HGV drivers to its skills shortage jobs list, to allow EU workers to fill the shortfall, were investigated but not implemented following pressure from the Home Office.
BP is said to have asked the Government for similar support temporarily.
Gordon Balmer, an executive director at the Petrol Retailers Association, which represents independent forecourts across the UK, said some sites are suffering from delays, particularly those in London and south-east England.
He recommended that motorists keep enough fuel in the tank to reach alternative filling stations in the "rare instance" that fuel is not available at the first one they visit.
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