Motorists are being urged not to panic-buy ahead of planned fuel tax protests, as queues of up to an hour are reported at some petrol stations.
Cars queue for petrol in Essex on Tuesday - Photo by Paul Wood
The Fuel Lobby's Andrew Spence said no oil refinery blockades were planned so there was no need to stock up.
Some petrol stations have reportedly "run dry", while others are employing extra staff to cope with the demand.
Merseyside Police have asked people not to ring 999 to ask where to buy fuel after phone lines became strained.
And there are reports of lines of motorists topping up their tanks in Kent, Lincolnshire, Manchester and long queues at station forecourts in east London.
Last week the government reportedly discussed plans to deal with a threat to fuel supplies - including the possibility of petrol rationing.
A Department of Trade and Industry document details possible measures including purchase limits, restricted opening hours, and moves to discourage motorists from frequently topping up their fuel tanks.
Mr Spence told BBC News it was this talk of rationing that had prompted motorists to stock up.
"There will be no blockades so, please, there is no need to panic-buy."
He also urged Chancellor Gordon Brown to cut tax immediately.
Mr Spence said peaceful protests planned for Wednesday were an act of desperation from haulage and farming industries facing collapse.
They would also be supported by French, Spanish and American truckers, he said.
Petrol Retailers Association director Ray Holloway said there had been a day of increased sales and urged the government to set a pre-emptive "minimum fuel purchase".
That would prevent drivers with nearly-full tanks needlessly queuing, as many did during the fuel protests in 2000, he said.
He also warned motorists to behave responsibly: "I really do appeal to people to actually just buy fuel when they need it.
"If people really do buy in the normal way, fuel will be available on the forecourts."
There were now 25% fewer filling stations across the UK than in 2000, he told BBC News.
Protests against the fuel tax are being planned after the price of unleaded reached £1 a litre in parts of the UK.
But few believe the demonstrations would be on the scale of those that left many motorists without fuel and supermarket shelves empty five years ago.
BP, which operates 1,300 filling stations, said there were no signs of abnormal sales. This was reflected by supermarket chain Asda, which runs 146 stations.
Mark Bradshaw, head of Garagewatch, which represents 6,500 independent retailers in the UK, said forecourts had been "quite quiet".
Protesters were not intending to halt deliveries, so there was no need to panic, he added.
But Mr Bradshaw is calling for a tax cut and a "maximum figure on the pump of 80p a litre".
"With the barrel price of oil at a record high now the government are making huge amounts of revenue from North Sea oil.
"On top of that the higher the price at the pump, the more they are making on VAT as well."
Institute of Directors chief economist Graham Leach also called for a tax cut pointing out that 47p of the 97p pump price went into Treasury coffers.
Liberal Democrat shadow chancellor Vince Cable said there was no justification for panic-buying but said "the government needs to have contingency plans in place".
Facts and figures behind UK petrol price rises
Roger King, chief executive of the Road Haulage Association, said there was a "very strong case" for the government to reduce fuel duty, particularly for commercial vehicle operators.