TSB plans to close its branch in West Street, Brighton, at the end of June next year.
The branch is one of 164 earmarked for closure, with about 900 job losses expected as a result.
The other TSB branch in Brighton – in Western Road – is to remain open.
The bank said that more customers had switched to using digital services although it planned to retain 290 branches around the country.
TSB, which is owned by Banco Sabadell, the Spanish bank, also said that staff losing their jobs would where possible be those who took voluntary redundancy.
Yesterday (Wednesday 30 September) the company said: “The changes have been driven by a significant shift in customer behaviour, including a reduction in the number of customers using branches and a significant acceleration in digital adoption.
“As part of TSB’s strategy, the bank had previously set out its intention to reduce its branch network in order to remain competitive compared to the wider industry.
“These changes today accelerate the pace of the overall branch transformation.”
TSB chief executive Debbie Crosbie said: “Closing any of our branches is never an easy decision but our customers are banking differently – with a marked shift to digital banking.
“We are reshaping our business to transform the customer experience and set us up for the future.
“This means having the right balance between branches on the high street and our digital platforms, enabling us to offer the very best experience for our personal and business customers across the UK.
“We remain committed to our branch network and will retain one of the largest in the UK.”
TSB customer banking director Robin Bulloch said: “Alongside these changes, we will continue to invest in our remaining branch network to offer high-quality banking services, fully integrated with improved digital capability.
“We are working to ensure the transition towards digital – which is being seen right across the economy – is handled sensitively and pragmatically for our colleagues and customers.
“We’re taking steps to support vulnerable customers and those in rural locations.”
The bank said: “Branches earmarked for closure have been selected to ensure 94 per cent of TSB customers can travel in 20 minutes or less to a branch – and the new network will have an average of 17,000 customers per branch, which remains below the UK average.
“The network will be the seventh largest in the UK.
“In addition, TSB is further enhancing its partnership with the Post Office including adding the ability to deposit and withdraw cash using a card, for both business and personal customers, and collect coin change from pre-agreed locations.”