Dorset police have ordered all petrol stations in the county to close after big queues from panic buyers began to create hazards to other road users.
There are sporadic reports across the country of panic buyers emptying a small number of petrol stations ahead of a planned strike by fuel tanker drivers - despite there being no actual threat to the fuel supply.
"There is no disruption to the fuel supply in the UK and members of the public should not panic buy," Dorset police chief insp Nick Maton said.
"The actions of some motorists in queuing irresponsibly at petrol stations is causing danger to other road users.
"Police are taking action, requesting petrol stations to close temporarily in order to keep traffic flowing.
"Once the queues have dispersed, the petrol stations may reopen for short periods."
The government caused confusion over the fuel supply when both cabinet office minister Francis Maude and Prime Minister David Cameron told motorists it would be sensible to take precautions and fill up their tanks if they had a chance, though not to rush since there was no immediate threat.
Motoring group the AA called the government's response the "height of irresponsibility".
Fuel tanker drivers who are part of the Unite union voted to strike in a row with oil companies over pensions, working conditions and safety concerns.
A date for the strike has yet to be set and the union must give seven days' notice before its members walk out.