Southfields Library has been reopened to the public following £16,000 roof works.
The library was recently swamped with controversy when Councillor Malcolm Grimston left the Tory party amid concerns it could close.
The council insisted there were absolutely no plans to close the library.
Community services spokesman, Councillor Jonathan Cook, said: "Wandsworth Council is investing in its libraries at a time when many other local authorities are closing theirs."
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