But one regular customer said the service was "vital" and the closure would inconvenience those who don't use mobile or internet banking.
Barclays announced today that the branch in Market Street will close on April 17.
Adrian Davies, market director for Barclays, said: “The way customers undertake their banking is changing as people increasingly use online, telephone and mobile devices.
"At Barclays Oakengates branch, customer usage has continued to fall by 13 per cent and 85 per cent of our customers now use telephone and online banking, which is why we have taken the difficult decision to close it.
"We hope that the availability of our nearby Barclays branches at Telford Town Centre branch, Wellington and Madeley, along with our range of digital channels, will help to ease the transition for our customers.”
A document from the Barclays website said: "The number of transactions [at the Oakengates branch] has gone down in the previous 24 months, and additionally 85 per cent of our branch customers also use other ways to do their banking such as online and by telephone.
"Customers using other ways to do their banking has increased by 27 per cent since 2012.
"In the past 12 months, 70 per cent of this branch's customers have been using neighbouring branches.
"We've identified that only 105 customers use this branch exclusively for their banking.
"Before we make the decision to close any branch, we think carefully about how it has been used so far.
"We consider how many customers have been visiting, what kind of transactions they've been making, and all the other ways they've been choosing to bank with us. We also take into consideration the availability of other branches in the wider community."
A customer who did not want to be named said that Oakengates residents wanting to do their banking would now have to go to the centre of Telford.
He said: "It is the last bank in Oakengates. It's pretty vital, especially for those that wouldn't do online banking or mobile banking.
"The nearest one is at the town centre but you have to pay for parking at the town centre.
"You're going to be paying for your banking really."
He said that the Oakengates branch was always busy when he visited.