Some 800 households in the Camden area of London will be moved to temporary housing.
Initially the council had said only Taplow Tower would be evacuated and Sky News Reporter Dan Whitehead said the scene there was one of "confusion".
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.
"My thoughts are with residents being evacuated in Camden while their homes are made safe tonight", she said.
The rest centre is at Swiss Cottage library, she said, adding: "People are on the ground now talking to residents, working with them to move them to the rest centre".
The move comes as a vast operation is under way across the United Kingdom to identify buildings with cladding like that used on the Grenfell Tower fire in north Kensington where a fire killed at least 79 people.
"Preliminary tests show the insulation samples collected from Grenfell tower combusted soon after the test started", McCormack said.
Camden is one of the councils in England which has learned that combustible cladding has been placed on buildings during renovation projects, though they had ordered non-flammable cladding.More news: All US big banks well capitalized, Fed stress tests show
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The US-based company said that consumers who bought Hotpoint fridge-freezer models FF175BP or FF175BG should contact the company "so that we can register their details and contact them with further information".
Firefighters and emergency workers who battled the inferno have been leaving messages and tributes to the victims at a makeshift memorial near the charred apartment block.
A United Kingdom fire service spokesman said a failed cladding test did not necessarily mean a building was unsafe and it would depend on amount of cladding and where it was fitted.
Tauranga mayor Greg Brownless said: "Naturally it's concerning if any of our buildings are coated in the same material as the Grenfell Tower but fortunately we do not have many high rises in the city".
Heartbreaking messages written on red London Fire Brigade T-shirts offer poignant tributes alongside flowers, toys and candles.
Another firefighter wrote "Our hearts go out to everyone touched by this tragedy".
The letter says that the Army will be assisting with building repairs.
Teacher Kim Price, who lives in Blashford tower with her 14-year-old son, added: "I really don't know what to do, I'm so scared right now". Along with Manchester, only Camden and Plymouth have been identified among this list.