Householders are being warned that current safety standards for fridges and fridge-freezers may be "deficient", creating a potential fire risk.
Consumer group Which? says new, tighter standards due by 2019 should be brought in much faster.
The body responsible for those standards said it was working hard to introduce them as quickly as possible.
In the meantime, Which? says, the current tests used are insufficient and do not replicate a real house fire.
In more stringent testing it carried out itself, Which? found that fridges with plastic backs were highly flammable.
Two samples were subjected to an open flame and caught fire after 10 seconds.
Under this particular test, the samples should be able to withstand a flame for at least 30 seconds.
"This once again shows that the UK's product safety regime is simply not fit for purpose and the government can no longer continue to allow it to fail," said Alex Neill, managing director of Which? home and product services.
The British Standards Institution (BSI), which is responsible for standards, said it had already tightened up the rules on the way that fridges and freezers are tested.
However, it will be more than a year before those rules come into force.
"BSI has been a driving force in getting more stringent fire safety requirements included in any revision of the standard at both European and international level," said Scott Steedman, director of standards at BSI .
"We have already achieved a certain level of changes made in the newly amended international standard."
Which? conceded that fires caused by fridges and freezers are very rare.
Of fires that are caused by faulty appliances, only 7% are caused by a fridge or freezer (see chart above).
And as yet, there are no known cases where such a fire has proved fatal.
A Hotpoint fridge-freezer was cited by police as a cause of the Grenfell Tower tragedy, which killed 71 people, but it is not yet known whether it had a flammable back.
Which? has also said that such appliances do not generally cause a fire to start, although they can help it to spread.
Which? has already advised consumers not to buy fridges or freezers with plastic backs. In a list published earlier this year, it recommended householders chose metal or aluminium laminate-backed appliances instead.
It has also appealed to manufacturers to stop making appliances with plastic backs.
The London Fire Brigade has campaigned for a change in safety standards for more than five years.
The Association of Manufacturers of Domestic Appliances (AMDEA) said there were 43 million fridges and freezers in the UK and fires were rare.
A spokesperson said the issue was about fire retardancy, rather than the self-combustion of appliances themselves.