Petrol sales shot up by 81% and diesel by 43%, according to the Petrol Retailers Association, which represents about 5,500 garages across Britain.
Retailers said there was a surge in sales of jerry cans after a minister advised people to fill them with fuel, in comments he was later forced to retract.
Opposition Labour Party leader Ed Miliband called on prime minister David Cameron to apologise after the government issued a string of conflicting messages to motorists.
“The prime minister is presiding over a shambles on petrol. The country is paying the price for the incompetent way he is governing,” Mr Miliband said.
Police forces in several areas reported queues at petrol stations.
The county of Dorset said it had told some petrol stations to close temporarily because motorists were behaving “irresponsibly” and causing a danger to others.
“Police are taking action, requesting petrol stations to close temporarily in order to keep traffic flowing. Once the queues have dispersed, the petrol stations may reopen for short periods,” police said.
Emergency services in London and West Sussex said they had been called out to deal with spillages from people overfilling their vehicles.
The Automobile Association said there were “localised shortages, queues and some profiteering” at petrol stations.
Workers in five oil companies have already voted in favour of industrial action over terms, conditions and safety standards but have not yet set a date for a strike.
Negotiators said talks on the strike would not be held before Monday.
The government has said it is training up army tanker drivers to take over in case a strike goes ahead.
The government yesterday repeated its advice to people to keep stocked up with petrol, although it toned down the message.
Energy minister Ed Davey denied the government was creating panic. “Our major advice is that people just need to do the sensible thing if they’re going into the petrol station, they should get a full tank of petrol, not a half-tank of petrol, and they should top up where necessary.”
The fuel saga heated up on Wednesday when minister Francis Maude said motorists should fill up jerry cans with petrol.
Firefighters said his advice was dangerous — and illegal depending on the size of the cans involved — and the government retracted Maude’s advice yesterday.
The government’s words failed to assure motorists. Halfords, a motor supplies retailer, said sales of jerry cans had increased by 500%.
Meanwhile, holidaymakers travelling through Stansted airport during the Easter weekend face disruption after baggage handlers voted to strike in a row over pay.
The move follows an overwhelming vote in favour of industrial action by 150 GMB members employed by Swissport after the union claimed shift changes would lead to wage cuts of up to £1,000.
The union said strikes will be held on Good Friday, Easter Saturday and Easter Monday. The changes will require that baggage handlers travel to work an additional 13 times a year.
Official Gary Pearce said: “Up to now the company has been intent on imposing these changes without agreement and this is completely unacceptable, as this vote shows.
“GMB has offered several alternative shift patterns and working arrangements but the company refuses to listen so far.
“I have notified Swissport of the ballot result and I have asked them for more talks to try to avert action over these pay cuts.
“GMB members consider that Swissport is attempting to make savings at their expense and they are not willing to agree to this.
“Unless there is urgent talks and a settlement, this vote for action this will result in disruption over the Easter Bank Holiday weekend,” Pearce said.
“If the strike goes ahead, Swissport is entirely to blame for the disruption.”