Unite said that 460 jobs were at risk across the country, with Leeds highlighted as one of the several areas at risk of job losses.
The bank is relocating hundreds of jobs to its central offices in Glasgow, Manchester and Northampton, and say there will only be a loss of around 50 jobs, with 400 moving to the three bigger centres.
The news comes five days after British Gas announced they were closing their Armley offices, with Leeds staff's jobs to go.
A Barclays spokesman said: "In order to best serve our customers and clients Barclays is moving teams closer together at our core UK sites in Glasgow, Greater Manchester and Northampton, where we are investing in new campuses and office space.
"Today we have informed staff that a number of operations and technology roles are relocating within the UK."
The exact figure for jobs at risk in Leeds is unclear, although the city is not one of the biggest areas of risk. Birmingham and Coventry are the main areas set for major job losses, and Stockton-upon-Tees, Manchester, Canary Wharf, Liverpool, Northampton, Cardiff, Poole and Petersfield are also at risk.
-> British Gas to close Canal Street offices in ArmleyThe Barclay's spokesman added: "We are not reducing the number of jobs overall, except in a few cases of duplication, and we will remain a significant employer in both Coventry and Birmingham."
Dominic Hook, national officer at Unite, said news of the job reductions was "extremely alarming".
He said: "Unite is very clear that the decision to cut around 460 jobs will result in a large number of compulsory redundancies which will bring a noticeable impact on customer service across Barclays.
"The decision by Barclays to make significant job losses in the West Midlands is a huge blow for the workforce. This is even more alarming in light of 170 staff from fraud operations were cut in Coventry last year.
"Unite is in discussion with Barclays regarding its future site strategy in order to gain vital clarity and job security for the workforce.
"The union has challenged the bank on service quality levels due to the loss of knowledge and experienced staff as a result of these changes."