Firefighters tackle the blaze at the Cambridge Road Estate in Kingston. Picture by Joanna Cockle.
Kingston Council has set up a rest centre in Piper Hall, in Cambridge Gardens, for those displaced and in need of shelter.
A spokesman said: "We are only in the first hour or so, so we have made initial preparations on the basis that some people will be out of the building and in need of some rest. In terms of numbers, or long-term implications, it's too early to say."
They said social services and a homeless unit would be on hand.
Thais Portilho-Shrimpton said: "There is a giant column of smoke, I'm walking towards it now.
"There's a helicopter above one of the towers, they might be taking people out of the building."
Comments: Our rules
We want our comments to be a lively and valuable part of our community - a place where readers can debate and engage with the most important local issues. The ability to comment on our stories is a privilege, not a right, however, and that privilege may be withdrawn if it is abused or misused.
Please report any comments that break our rules.
Read the rules here