The TSB branches in Milngavie and Bishopbriggs are among 17 Scottish branches the bank has confirmed it will close next year.
Bishopbriggs has already lost its Clydesdale and Royal Bank of Scotland branches in recent years.
Local councillor Alan Moir said: “I am extremely disappointed by this decision but I am also furious with the years of developer paralysis.
“The stop start indications of ‘imminent’ developments initiatives in and around the town centre are taking far far to long in getting a move on. I will be requesting an urgent meeting with senior council officers to see what immediate action can be taking and seek clarity from the main players who have such a significant influence on Bishopbriggs Town Centres future.
“Below is the correspondence I received from TSB this afternoon outlying their reasons for this closure announcement specifically referencing the Bishopbriggs branch.”
A letter from the bank to Councillor Moir states the Bishopbriggs branch is “no longer viable” as transactions have dropped by 11 per cent since 2016 and only 13 customers visit every week.
Meanwhile, the number of people using online or mobile banking has risen by seven per cent and 89 per cent of customers in Bishopbriggs use another branch or mobile or telephone banking. Also, the majority of customers at the branch with business accounts use a different branch for their banking.
The closest remaining branch of TSB to Bishopbriggs is 1.6 miles away in Springburn, and the local post office also provides financial services.
The letter continues: “Our focus now is on helping customers at Bishopbriggs adjust to this transition, particularly the most vulnerable. We are very conscious that some consumers may feel left behind by the pace of change in banking.
“That is why we are launching new programmes to provide extra support to those customers who rely on branch banking the most and why we are working with stakeholders to find new ways to support customers and the communities we serve including:
“Tailored one-to-ones for customers that regularly use the branch to help them continue to perform day-to-day banking tasks in the local area.
“New workshops in branch for personal and business customers to help build knowledge and confidence with digital banking, telephone banking and local Post Office services.
“Our Telephone Banking service is available to customers and will be able to provide support and guidance in transitioning from their local branches.
“And where we cannot provide the support the customer needs, we will help them to switch provider.
“Centrally, we are working with government and the industry to find a national solution to helping communities continue to access cash and banking services when a bank makes a decision to close.”