High street bank Lloyds TSB is to close its service centre in Plymouth with the loss of 126 jobs.
The news followed announcements last month that 37 jobs were to be lost in Plymouth and 42 in Exeter from other operations by the company.
The Lloyds TSB Group Union said the closure of the Plymouth centre was directly linked to the bank's strategy of moving some of its work to India.
The bank said that this was "absolutely" not the case.
It said it was part of a nationwide restructuring to consolidate its workforce at a number of larger sites.
The bank said it would try and avoid redundancies, and would be speaking to all staff individually to try and find them work elsewhere.
It added that its service to Devon customers would not be affected.
Union members will be in the city on Wednesday asking customers to sign a petition calling for an end to the transfer of work away from the South West.
Meanwhile, 113 workers will be laid off when a food factory closes in east Devon in July.
The 2 Sisters Food Group is cutting the posts at its chicken processing plant in Blundell Road in Tiverton.
Workers said they were given no indication about redundancies. The West Midlands-based company said it would try to help sacked workers find new work in the area and it was working with local employment offices.