Detective Superintendent Fiona McCormack said that in view of the heavy death toll, police were considering manslaughter charges over the disaster.
She said the Hotpoint model, FF175BP, involved was not subject to recall and the manufacturer was doing further tests.
"We now have expert evidence that the fire was not started deliberately," McCormack told reporters in London.
Britain ordered an immediate technical examination of the Hotpoint fridge model to establish whether further action needed to be taken, but said there was no need for owners to switch off their appliances.
Whirlpool Corp, the world's largest maker of home appliances, owns the Hotpoint brand in the Europe and Asia Pacific regions. In the United States, the brand now belongs to Haier, following the Chinese group's purchase of General Electric Co's appliance business.
A spokesman for Whirlpool could not be immediately reached out of US business hours.
"Preliminary tests show the insulation samples collected from Grenfell tower combusted soon after the test started," McCormack said.
Such were their concerns after the tests that the information was immediately shared with government to disseminate more widely.
"Given the deaths of so many people we are considering manslaughter as well as criminal offences and breaches of legislation and regulations," McCormack said.
The blaze, Britain's worst since World War Two, has heaped pressure on Prime Minister Theresa May, already fighting for her political survival after her party lost its parliamentary majority in a snap election on June 8.
When speaking about the 79 people dead or missing, presumed dead, McCormack said: "I fear that there are more."