The National Fire Chiefs Council (NFCC) - which includes Shropshire Fire and Rescue Service - says storing fuel in a car, the workplace or at home risks more blazes, which put their services at risk.
It a statement issued on Tuesday the NFCC said fuel vapour can cause "irritation of the eyes, nose and throat, and exposure to high concentrations, particularly in confined spaces, can cause dizziness and unconsciousness."
"Storing fuel in a car, the workplace or at home can create a fire hazard due to its highly flammable and combustible nature. This can cause a serious risk of injury, loss of life and damage to not only people’s properties but to others in the vicinity."
The NFCC says the law also clearly states only 30 litres of petrol can be stored at home or at non workplace premises without having to inform the local Petroleum Enforcement Authority (PEA).
"Stockpiling could also put unnecessary pressure on fire and rescue services across the country if there is an increase in fuel related fires and incidents," the NFCC said.
The law allows people to store certain amounts in different types of containers.
The NFCC is also urging those who may have brought additional fuel to take extra precautions, including:
No smoking and no naked lights in the vicinity.
Decant fuel in the open air - not inside a garage or shed.
Use a pouring spout or funnel.
If clothing is splashed with fuel, change it immediately.
Fuel expands and vapour can build up in hot weather, so avoid filling to the brim.
Approved containers should not be overfilled and should be securely fastened during transit to prevent them falling over and leaking.
Spillages on the road surface, particularly of diesel, create slippery conditions that are a major hazard to other road users - especially those on two wheels.
Meanwhile there is no sign yet of the rush to the pumps ending, with social media posts leading to people rushing to fill up "like bees to a honey pot".
The oil companies have said they expect the pressure on forecourts to ease in the coming days, with many cars carrying more fuel than usual.
However the chairman of the Petrol Retailers Association (PRA), Brian Madderson, said that there was little sign of that happening - with social media driving the dash to the pumps.
"Disappointingly the messages I'm getting this morning from our retailers are that panic buying does continue," he told the BBC Radio 4 Today programme.
"One of the reasons for this is social media. As soon as the tanker arrives at a filling station people on social media are advising that a tanker has arrived and it is like bees to a honey pot."