The strike ballot over terms and conditions was held by the Unite union.
The government is holding a meeting with fuel delivery companies and supermarkets to work out a strategy to deal with any strike.
Army drivers are being trained to deliver fuel to petrol stations.
Cabinet Office minister Francis Maude said the government had "learnt the lessons" of the past and stood "ready to act" in case of a walkout.
Unite said the government should be putting pressure on oil companies.
Len McCluskey, Unite's general secretary, said: "For over a year we've been desperately trying to bring about some stability in the sector and urging government ministers to persuade contractors and oil companies to engage in meaningful discussions with us."