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The council said it could take two to four weeks for the four blocks to be made safe.
The site said the Chalcots project was a £66 million refurbishment which lasted 191 weeks.
Up to 40,000 people from 34 tower blocks now face evacuation after cladding in 17 council authorities throughout England failed new fire tests.
The number of evacuations currently stands on 20,000, with about half of the 600 potentially-dangerous high rises had been tested by Friday evening.
Some 3,000 Chalcots residents face weeks in temporary accommodation after Camden Council leader Georgia Gould said the authority took the 'extraordinary action' to clear 600 flats because 'we are really clear that those four blocks are not safe'.
London Fire Brigade inspecting officers identified concerns over the combination of external cladding, fire doors, gas pipes and insulation, she added.
The buildings are located in 17 local authorities across the country, including Manchester, Plymouth, Portsmouth, and Camden, Barnet, Brent, and Hounslow, in London.
The number rose from 34 tower blocks across 17 local authorities.
The Department for Communities and Local Government (DCLG) said Doncaster, Norwich, Stockton-on-Tees and Sunderland all had buildings that failed tests, while Manchester, Plymouth and Portsmouth have already been named.
Islington, Lambeth and Wandsworth joined Barnet, Brent, Camden and Hounslow on the growing list of London boroughs, while 11 other areas are yet to be named.
But despite being urged to leave by officials, around 20 households had refused to vacate their homes, in Taplow, Burnham, Bray and Dorney blocks, by Saturday evening.
On Sunday, Ms Gould said: 'This morning council staff will conduct further door knocking to ask those who remain to leave, and issue another letter reiterating to residents who are still remaining in the Taplow, Bray, Dorney and Burnham blocks, that they must leave.'By remaining in the blocks these residents risk delaying the work that is required and that we are undertaking to make these homes safe.'It is not safe to remain in these blocks and our residents' safety will continue to be the council's number one priority.'The Grenfell, in which at least 79 people are believed to have died, has raised questions about cheap, flammable cladding.