The TSB branch in Clapham is set to close in September 2024, as part of the banking group's latest round of closures.
TSB is shutting 36 branches across the UK, in an effort to move towards a "better balance" of digital and face-to-face services.
It said the majority of its customers are now banking digitally.
The banking group has already closed 10 branches over the past year, and these closures will leave the group with 175 branches and other banking services.
Another London branch set to close is the Bethnal Green branch.
Locations closing in September 2024 also include Alloa, Birmingham, Carmarthen, Dovercourt, Glasgow, and Manchester, among others.
Branches set to shut down in May 2025 include Amble, Flint, Tenbury Wells, and Whitchurch.
The full list of closures was announced on Wednesday, May 8.
The banking group is also cutting 250 jobs across the business.
A spokesman for TSB said: "The decision to close a branch is never taken lightly, but our customers are now doing most of their banking digitally and we need to move to a better balance of digital and face-to-face services.
"We remain committed to a national branch network and through innovation and integration with video, telephone, digital, branch and other face-to-face services TSB customers have more ways to bank with us than ever before."
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