Ludlow MP Mr Dunne, along with Shropshire council and town council representatives from both towns, met Barclays representatives in Ludlow to make a case for the banks to remain.
Mr Dunne said Barclays had made the decision the banks were going before the meeting.
"Each of the local representatives made their case for why the banks should not be closed," he said.
"There's been very significant support shown in Much Wenlock both online and in petition form. The petition has had more than 800 signatures and we also handed in 150 surveys.
"There was also a second petition in Church Stretton but it had not been completed.
"We expressed particular concern about the loss of the ATMs as the banks serve a very elderly population in both towns and the surrounding areas. Many of the people rely heavily on face-to-face, over the counter contact.
"The bank gave us some statistics and said that less than 100 people in Church Stretton and less than 50 people in Much Wenlock solely use the bank in store.
"Now the options for those people will just be to use the post office. In both cases the post office staff will need training to cope with the increase in complex transactions.
"However, they are keen to work with the local representatives to try and help vulnerable customers to ensure they access to facilities."
Barclays is willing to provide an ATM machine in Much Wenlock, according to Mr Dunne after the meeting yesterday afternoon.
He said: "In relation to Much Wenlock, Barclays acknowledged that there was a mistake in relation to the calculation of the number of ATM machines, so they were prepared to make some provision for that if the town council can come up with a place for it to go.
"We made as strong case as we could to keep the banks open but it was crystal clear Barclays had made up their minds before the meeting.
"I was pleased they made an offer to provide an ATM in Much Wenlock."