Nearly a third of BP’s British petrol stations have run out of the two main grades of fuel, the oil company said.
Motorists queued up at petrol stations over the weekend as Brits panic-bought fuel despite ministers’ insistence that there was no shortage.
Oil firms had reported that a lack of delivery drivers was causing transport problems from refineries to forecourts.
Some operators have had to ration supplies and others to close gas stations.
“With the intense demand seen over the past two days, we estimate that around 30 per cent of sites in this network do not currently have either of the main grades of fuel,” BP, which operates 1,200 sites in the UK, said on Sunday.
The company said it was working to resupply “as rapidly as possible.”
Transport secretary Grant Shapps said shortages were simply caused by panic buying and would resolve itself shortly.
“There’s plenty of fuel, there’s no shortage of the fuel within the country,” Shapps told Sky News.
“So the most important thing is actually that people carry on as they normally would and fill up their cars when they normally would, then you won’t have queues and you won’t have shortages at the pump either.”
The Department for Transport announced it would make 5,000 visas available to HGV drivers and 5,500 available to poultry workers until Christmas.
The government also said on Saturday that it would train up to 4,000 people as new HGV drivers over the next 12 weeks.
Other measures include writing to almost 1m drivers who currently hold a HGV driving licence, to urge them back into the sector.
Industry bosses said the measures were not enough to solve a shortfall of around 100,000 drivers and urged for further action.