Drivers queued for fuel at some gas stations on Tuesday as supply disruption fears grew although retailers claim no problems yet.
The rush to fill up came after media reports that demonstrators who brought the country to a standstill five years ago by blockading oil refineries planned repeat protests against high fuel prices this week.
"Customers watching the television news and reading the papers feel they need to top up, but there's no need," said a spokesman for retailer Tesco, which has 380 filling stations dotted around the country.
"There are absolutely no supply problems so our message to customers is not to change their buying patterns," he said.
There was a similar message from rival supermarket chain ASDA and oil company BP, which is the country's largest fuel retailer with about 17 percent of the market.
While some commuters reported early morning queues in some parts of the country, other motorists driving into the capital on Tuesday morning filled up without a wait.
According to local media, a group called the Fuel Lobby is planning to blockade oil refineries across Britain from Wednesday morning to protest against increases in petrol prices.
The cost of a litre of petrol climbed above a pound in some parts of the country last week after the price of oil on world markets hit a record of more than $70 a barrel.
Truck drivers fear that if they turn up at a refinery where there is a blockade they could run the risk of losing their licences because police think they are involved.
"We want to bring to the attention of the government that the people are not very happy with the tax system on fuel in this country," (Reuters quoted Alan Greene, organiser of the Welsh campaign for Less Fuel on Tax as saying.