The high-rise buildings on the Chalcots estate in Camden were being emptied on Friday evening after firefighters said they "could not guarantee our residents' safety", local council leader Georgia Gould said.
Detective Superintendent Fiona McCormack also said experts had now concluded the fire, the mostly deadly blaze in London since World War Two, had started in a fridge freezer.
English authorities determined that a Whirlpool refrigerator with the brand name Hotpoint ignited the fire in the Grenfell Tower that resulted in the deaths or presumed deaths of at least 79 people.
Grenfell Tower, in north Kensington, west London, had undergone an 8.7 million pound ($11 million) refurbishment which was completed in 2016, but residents of the more than 120 apartments had complained about its fire safety.
She added: 'Together we decided that the Taplow block needs to be temporarily decanted while we undertake urgent fire safety works so that residents can be fully assured of their safety.
The U.K. government has issued an order for an immediate examination of all such units in order to determine whether or not they pose a fire risk as well.
They will be moved to temporary housing, which includes hotels and homes of friends and family.
Investigators have listened to more than 600 emergency calls - and "some of those calls are over an hour long and each call tells its own distressing story", she said. She said it would examine all aspects of the cladding: the aluminium tiles, the insulation behind it, how it was fitted to building and the installation.
Police are looking at all parts of the cladding system and its installation, McCormack said.
"What we are being told at the moment by the Building Research Establishment is that the cladding and insulation failed all safety tests".
Housing trust Wythenshawe Community Housing Group has started work to remove 78 feature panels at its Village 135 scheme that were identified as using similar material to the cladding panels used at Grenfell Tower.
McCormack also repeated calls for anyone with information about the fire and all those in the tower at the time to come forward as police continue to comb through the devastated building to try to identify all the victims. Samples from 14 buildings in London, Manchester and Plymouth have already been found to be combustible.
McCormack said she feared more people could have been killed in the fire amid concerns some of the people living there had been in the country illegally.