Ministers have held crisis talks with haulage bosses after panic-buying saw sales of unleaded petrol shoot up by 172%.
The Retail Motor Industry Federation - which represents independent petrol stations - said that sales on Thursday nearly doubled when compared to a regular Thursday.
Diesel sales were up by 77%, the federation said.
"Panic-buying continues, with surging demand at forecourts," Brian Madderson, of the Retail Motor Industry, said.
"Starting slowly on Monday, motorists and business users have pushed up demand rapidly over just four days to yesterday's unsustainable levels."
Meanwhile, the Government discussed contingency plans with company bosses to try to mitigate the effects of any walkout by tanker drivers.
Energy Secretary Ed Davey - who has advised drivers who usually only fill their tanks by one-third should consider upping this to two-thirds - lead the talks.
After the meeting in Whitehall, an Energy Department spokesman said: "Discussions focused on contingency planning, covering training more military drivers in the event that a strike is called.
"There is no strike at the moment, and we are calling for a swift resolution to this industrial dispute."
Conciliation talks between the Unite union and the seven distribution companies at negotiating service Acas will not take place before Monday .
Acas had previously hoped to bring the sides to the table earlier this week.
As the union must give seven days' notice before any strike date is set, Unite on Friday rule out any action over Easter.
Unite's assistant general secretary Diana Holland defended the union against accusations it could have done more to halt the panic-buying of fuel.
"We have never done anything to suggest we were searching for anything other than a negotiated solution and to avoid the need for industrial action if we could," she told Sky News.
"What we are calling on the Government to do is to support finding a negotiated settlement and play their part in calming things down."
Prime Minister David Cameron will chair another meeting of the Cobra committee later today - the second of the emergency planning group of ministers since the fuel panic flared.
Despite the fact that no strike has been called some petrol stations have been forced to close as motorists rush to fill up their cars.
Panic-buying by motorists on Thursday brought in £32m extra in fuel excise duty for the Treasury, the AA calculated.
The Petrol Retailers Association, which represents around 5,500 garages, blamed advice from the Government on keeping tanks topped up, including the much-criticised call by cabinet office minister Francis Maude to fill up jerry cans.
A spokesman said: "This is exactly what we didn't want - people panic-buying.
"Deliveries are still being made to garages and we are advising people to continue with their normal buying habits."
AA president Edmund King described the spate of petrol stations run dry as "self-inflicted".
He said: "There is no fuel tanker strike and therefore if drivers followed normal fuel-buying patterns there would be no fuel shortage whatsoever."
Professor Stephen Glaister, director of the RAC Foundation, said confiormation that the strike would now not take place until after Easter would be "a great relief" to motorists.
"It should give everyone breathing space and ease the pressure at the pumps."
Unite represents around 2,000 drivers in seven distribution companies, although union members in two of the firms voted against strikes.
The seven firms account for 90% of the supply to UK forecourts.