The Teddington NatWest branch is due to close in October as the company closes branches across the country amounting to job losses of around 470.
The closures are due to a “dramatic shift” in the way that customers use the bank – with a switch to people banking online or through apps.
The branch is among 30 RBS branches and 128 NatWest branches around the UK will close this year.
A spokesperson added: “As customers change the way they bank with us, we must change the way we serve them.
“The role of the branch is fast moving to a centre for advice, away from basic transactions.
“While the branch will still be a core part of our offering to customers, inevitably some branches will have to close.”
We will update this article as we have more information.