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We're being told there's no need to panic buy fuel, but queues have been reported across the South Coast, with some petrol stations having to shut.
It's after tanker drivers at five of the seven main supply companies have voted in favour of industrial action over terms and conditions, as well as safety standards.
Unite, which represents around 2,000 drivers who deliver to Shell, Esso and major supermarkets, is demanding minimum standards for pay, hours, holiday and redundancy.
The Army could be brought in to help drive supplies to petrol stations.
David Cameron's chaired a special COBRA meeting to discuss contingency plans, but the government says there is no need to panic buy.
AA president Edmund King said: "It's totally inappropriate for people to panic-buy. No strikes have yet been announced and there is enough fuel out there as long as people do not fill up unnecessarily."
However, some drivers appear not to be taking any chances. There have been queues reported at stations in Hampshire.