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.
HAVE YOUR SAY Have ensured that both mine and my wife's car is full, and made a special trip out to fill up my bike too
Paul Sealey, Cannock, England
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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.
Smaller scale?
"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".
It is just ridiculous to not step in now and bring those prices down
Garagewatch head Mark Bradshaw
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.
Revenue boost
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".
Although the groups remain united in their belief petrol prices are too high, it appears they are united by little else
Can the protests succeed?
"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".
PUMPED UP Facts and figures behind UK petrol price rises
At-a-glance
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.
Long queues outside a Birmingham petrol station, 12 September 2005.
Long queues are forming outside UK petrol stations as motorists rush to buy fuel ahead of protests against fuel tax.

Consumer groups such as 'The Fuel Lobby', the group behind the fuel protests in 2000, have given conflicting reports on plans to blockade refineries to prevent supply of petrol stations.  Action started at 6am this morning, with a low turnout of protesters at refineries.  Further protests are planned at forecourts and on various roads for the remainder of the week.  Welsh protesters plan a 20mph rolling roadblock on the M4 motorway, starting at 7am on Friday, September 16.

The government has told the public there are enough petrol supplies to last for 80 days, but petrol stations themselves may be set to run out much faster as large numbers of people fill up their tanks in anticipation of shortages. An eyewitness has said that as well as filling up their vehicle tanks, people are taking spare tanks. 

Bill Johnson, a petrol station manager in Cornwall, told the Guardian that he found it necessary to restrict petrol supplies to account holders only. He said: "They were shouting, 'You fucking bastards, I've got to get to work.' It wasn't pretty, people are just getting greedy."

Matthew Carrington of the Petrol Retailers' Association called on Gordon Brown to reduce tax.  "His tax take goes up as the price goes up, " he said.