The council had already announced it would immediately begin preparing to remove cladding from five towers on the estate discovered in checks following the fire in north Kensington which killed at least 79 people.
Camden Council initially said just some 161 households in the Taplow building on the estate were being "temporarily decanted" to allow up to four weeks of work to be done to the building.
Pictures of missing people on a message board near to the burnt Grenfell Tower apartment building standing testament to the recent fire in London, Friday, June 23, 2017.
Eleven buildings have now been identified as having combustible cladding such as that used on the Grenfell Tower.
"We realise that this is hugely distressing for everyone affected and we will be doing all we can, alongside the London Fire Brigade and other authorities, to support our residents at this hard time", Ms Gould said.
Deputy mayor Cllr Ann O'Byrne said: "We have a duty of care to residents to reassure them their buildings are safe, whether they live in a high or low rise block or one that has recently been refurbished".
Whirlpool, which owns Hotpoint, said, "We offer our most profound condolences to the victims, those who have lost loved ones, homes, and possessions, and to their friends and families".
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Documents and materials had been seized from a "number of organisations", she added.
The government has ordered an immediate examination of the refrigerator model that started the blaze.
The Chalcots estate has five tower blocks - four 22 storey blocks and one 18 storey block. From what we know so far, a unique set of circumstances combined and led to the Grenfell tragedy, but there is absolutely no room for complacency.
The announcement came as it was revealed manslaughter charges are being considered by detectives investigating the blaze in the tower in west London, which had failed fire safety tests.
Resident Michelle Urquhart says she's angry because residents were assured as late as Thursday that the problem was being addressed.
Nine of those who died on 14 June has been formally identified so far. The cladding is being studied amid fears that the panels fueled the fire in the 24-story building that was engulfed in less than an hour.
Tauranga City Council general manager environmental services Rebecca Perrett said the council was supporting the ministry's efforts. "We did our best I promise". Premier Inn said Friday it had "concerns" about the material on some of its buildings, though it is different to the type used on Grenfell.