The bank said it has not been immune to the effects of recent months, as low interest rates hit the income of all lenders.
More customers are also choosing to bank online, and making fewer transactions in branches, chief executive Andrew Bester said.
Bosses promised to try to redeploy staff where possible, and will consult with them and the unions.
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Rob MacGregor at Unite said that the union is “deeply disappointed” by the decision to cut staff and close branches.
He said: “Job losses are always unwelcome, however, given the repeated restructuring exercises that this workforce has been through over the past 10 years the news today will be particularly painful.
“During these extremely testing economic times, Unite wants all employers to work with the trade union to avoid job losses and protect the livelihoods of our members.
“Unite will continue to press The Co-operative Bank to put strategies in place to secure as many jobs as possible and avoid compulsory redundancies.”
The 18 branches will be closed by December 1 this year.
Co-operative Bank said it had chosen the sites after analysing their footfall over the last 12 months.
Mr Bester said: “Our people have shown great dedication and commitment to our customers over the past few months, so we are very sorry to announce this news today.
“Unfortunately, we’re not immune to the impact of recent events, with the historically low base rate affecting the income of all banks and a period of prolonged economic uncertainty ahead, which means it’s important we reduce costs and have the right-sized operating model in place for the future.
“At the same time, we are responding to the continuing shift of more and more customers choosing to bank online, with lower levels of transactions in branches, a trend which has been increasing for some time, across the banking sector and more broadly.”
Many of the UK’s biggest high street lenders have been at the centre of ensuring that businesses are supported through the Covid-19 crisis.
However, they have also been forced to write down many of the loans that they have given to businesses which may be struggling during the crisis.
Mr Bester added: “The bank is in a resilient position given the significant progress we’ve made in recent years, and our focus is on maintaining this as we continue to support our customers through the crisis. We will do all we can to support colleagues through the process with fairness and respect.”
The branches closing are:
City of London