Santander are to close three stores in Hampshire, including Romsey, Chandlers Ford and Lymington.
About 140 stores are closing in the UK, putting 1,270 jobs at risk.
The decision came in response to how customers are changing how they do their banking.
Romsey MP Caroline Nokes said: “I am very disappointed to hear Santander will be the latest financial institution to close a branch in Romsey, with the closest branch for my constituents being in Southampton.
“I am deeply concerned about the effect this will have on digitally excluded customers, who may not have access to online banking.”
Winchester MP Steve Brine said he was “very sorry to receive notice from Santander that they will close the branch at Fryern, Chandler’s Ford”.
He has urged anyone directly affected by the closure to get in contact with him.
Susan Allen, from Santander, said: “We will support customers of closing branches to find alternative ways to bank to suit their individual needs.”
The bank says it will help customers find other branches and access online, telephone and postal banking services.
The banking company is “working alongside the unions to support colleagues through the changes”.
At least a third of those at risk are expected to be placed in other jobs within the company.