Wem Town Council will write a second letter to NatWest despite being told it had no current plans to reverse its decision to close the branch in July.
Councillors are concerned about the effect the closure of the High Street branch will have on people in the area, especially the elderly.
The council has already written one letter to NatWest, calling for it to reconsider its decision and think about introducing shorter opening hours at the existing branch or a mobile banking service.
But the bank said in response that it currently had no plans to alter its decision, which has angered town councillors.
The issue was discussed at Thursday’s town council meeting where members voted to write a new letter to the bank.
Councillor Rosemary Dodd, newly-elected mayor of Wem, said: “We have received a letter back and are not happy with the response.
“They say the business has gone down 18 per cent since 2011 but if you average it out it’s not that much.
“They could have done what Barclays did and closed on one day but that doesn’t seem to be their policy.
“We asked about a mobile bank and cutting opening hours and they said they are not going to do that at the moment.
“They didn’t completely dismiss it and said they will think about it but there is no chance of that happening at the moment.
“We are going to pursue it. It is well used and I know businesses in the town are worried as are people who come into town from the countryside.
“Not everyone does online banking and we have got an ageing population in Wem,” she added.
Last month NatWest announced the closure would take place from July 13 due to a reduction in usage.
Bosses described it as a “difficult decision” but they would do all they could to answer customer questions in the lead-up to the closure.
The branch closure is one of several announced by major banks in the region in recent months. NatWest will also close its branch in Wellington and reduce hours at Bridgnorth, while HSBC has closed branches in Market Drayton, Chirk, Llanfyllin and Llanfair Caereinion.
Last month Whitchurch’s Co-operative bank also closed.
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