Tests are being carried out on about 600 high rises in England as 650 homes in tower blocks on an estate in Camden are evacuated.
The removals - across five boroughs - were agreed after cladding similar to that used on Grenfell Tower was found.
Aluminium composite material (ACM) in the cladding is thought to have been a factor in the fire's rapid spread.
A total of 79 people are either dead or missing presumed dead as a result of the Kensington blaze.
Barnet, Camden, Hounslow, Islington and Tower Hamlets councils are to remove cladding from tower blocks in their boroughs.
The presence of ACM has also been confirmed in tower blocks in Tottenham and Newham.
At the weekend it emerged ACM cladding should not be used on buildings above a height of 18m (59ft).
Cladding is typically fitted to the outside of high-rise buildings to improve insulation and tidy up the appearance of the exterior.
The Department for Communities and Local Government said 14 residential high-rise buildings in nine local authority areas had since been found to have cladding that raised safety concerns.
Councillor Richard Cornelius, leader of Barnet Council, said removing the cladding from three tower blocks in the area was a "precautionary measure".
"Although the exterior cladding panels are similar to those reportedly used at Grenfell Tower, the insulation materials behind the exterior panels are different and made from a non-combustible mineral fibre material," he said.
Hounslow Council said its cladding contained "rockwool", which is a "non-combustible product, unlike the case of the Grenfell Tower".
External thermal cladding will be removed from five tower blocks on Chalcots Estate.
Thermal cladding is to be removed from 11 London tower blocks as a precaution following the Grenfell Tower fire.