The South Shropshire MP has said that he is "appalled" by the bank's decision to close its Ludlow and Bridgnorth branches.
The reason for the closures is down to switch to online and mobile banking, with 80 and 83 per cent of customers at the Ludlow and Bridgnorth branches, using alternative ways to bank.
Mr Dunne said:“This is another example of Barclays choosing to abandon rural communities with further branch closures.
"Both Ludlow and Bridgnorth have a significant population of elderly and vulnerable people, who may not use the branch daily, but rely on a local branch presence when they need help and advice.
"With these closures, there will be no Barclays branches left in the Ludlow Constituency.
"I will be demanding a meeting with Barclays management to make the case for them to rethink these planned closures, and show they value their rural customers in South Shropshire.”
A spokesperson for Barclays bank said: "The role of the physical branch is evolving, with fewer than 10 per cent of transactions now taking place inside a branch.
"We will be engaging with local businesses and the wider community to discuss the alternative ways customers will be able to undertake their banking locally.
"And will be offering virtual ‘tea and teach’ sessions for customers wishing to explore digital banking and other alternatives to branch-based banking."