Urgent work was needed after masonry fell from a library in Hackney last month.
Scaffolding was put up outside Stoke Newington library last week.
The Grade II-listed library was built in 1892 and the council funded a £4.5m renovation before lockdown.
Plans include reopening the reference library to the public, layout changes, and a new base for the community service, which delivers books and DVDs to people who cannot get to the library.
The library has been extended twice – once in 1904 with money from philanthropist Andrew Carnegie and again in 1922 to house the World War One memorial hall.
The red brick building has stone dressings and was listed as “an early and good example of a borough library”, according to Historic England.
A Hackney Council spokesperson said: “We cordoned off the pavement outside Stoke Newington Library on 17 January after a piece of masonry was reported to have fallen from the building.
“Scaffolding was erected last week to help us check what repair work is needed. Once all surveys are completed, the extent of the work and associated costs will be confirmed.”
The cabinet approved the renovation work last October.
A Town Hall report said: “The renovation is aimed at repairing the various defects found with the roof and in the building and remediate interior damage in public spaces.
“The intended work will design and implement conservation-standard repairs to the structure which will ensure that it remains watertight and in sound condition for years to come.”
Rainwater had got into the building, causing damage, and the council report said it “has fallen into poor repair throughout”.
Work was also needed on “significant ‘back of house’ areas” which were “unsuited to present use” and a large area which was rarely used but could be a performance space.
Councillors approved a five-year programme of works.