Hammersmith Bridge could cost £120m to repair, engineers have estimated as the first stage of work begins.
The 132-year-old bridge was closed indefinitely to motorists in April after "critical faults" in the cast iron casing were found.
Transport for London (TfL) has financed the first £25m of the project but the main funding source has yet to be decided.
The work is expected to take three years to complete.
Hammersmith & Fulham Council is working with TfL to secure funding for the next phase of repairs in spring 2020.
The £120m estimate could change due to the "unknowns, complexities and challenges" of the bridge, the authority said.
Council leader Stephen Cowan said there had been "significant failings" in the bridge structure which has seen cracks appear in some of the pedestals.
"We're focused on getting the bridge reopened to cars and buses as quickly as possible", he added.