The authority said “significant” work has been undertaken at South Woodford Library and Gym to allow building work to start soon.
A confirmed reopening date will be announced in due course, according to a council spokesperson.
Until then, the gym and studio are relocated to Redbridge Drama Centre temporarily, alongside a pop-up library.
Residents are encouraged to visit the newly refurbished Woodford Green Library and Gym.
Fullwell Cross Leisure Centre and Kenneth More Theatre were closed after inspections also identified the presence of reinforced autoclaved aerated concrete (RAAC) there.
The lightweight material, commonly used in construction between the 1950s and 1990s, deteriorates over time.
Fullwell Cross Leisure Centre has reopened areas including the spa, reception and studios.
Group exercise classes now take place in Studio 1 and the Sam Ryan Studio.
The swimming pool remains closed, with sessions relocated to Loxford and Mayfield Leisure Centres.
The council spokesperson said: “Enhanced monitoring and signage have been installed to ensure safety, and disruption has been minimised by automatic membership pauses, relocated swimming lessons, and access to other leisure facilities in the borough.
“Council officers are developing a comprehensive remediation plan, including immediate repairs and long-term improvements to secure the facility’s future.”
Kenneth More Theatre’s auditorium remains out of service, but the bars, foyers, and studio spaces are open for hire.
Councillor Namreen Chaudhry, cabinet member for leisure, culture and communities, said: “We understand how important these facilities are to our residents and recognise the impact these temporary closures have caused.
“The good news is that a range of activities remain available at Fullwell Cross Leisure Centre, including exercise classes and the hugely popular spa facility.
“Kenneth More Theatre continues to operate as a hire venue, and construction will shortly begin at South Woodford Library and Gym.
“We’re committed to keeping our community updated and will share a confirmed timeline for the next phase of works as soon as possible.”
