Shocked staff were summoned to a meeting by managers yesterday to be told that 244 jobs are to go at the bank's only Scottish PPI centre, which is due to close next year.
The workload for dealing with the thousands of claims is to be absorbed by the company's centres in Sunderland, Liverpool and its London headquarters.
Dominic Hook, a national officer with the union Unite, said: "The workforce in Glasgow will be justifiably angry, and will feel that they have been betrayed.
"They have been working hard to resolve the problems caused by the mis-selling of payment protection insurance, but now they are being told they could lose their jobs."
Mr Hook said the staff had been a huge asset to the bank in dealing with the fall-out from the insurance claims.
He added: "We're demanding that the company does everything possible to avoid compulsory redundancies. Barclays has a duty to the workforce and it must leave no stone unturned in its search to find alternatives to redundancies."
A total of 244 workers are based at the centre in Nelson Mandela Place, with 137 permanent and 107 temporary.
A Barclays spokesman said: "In the last three years, Barclays has invested significantly in resolving PPI cases, including a designated centre in Glasgow.
"The volume of PPI cases has fallen and this reduction means the centre's role has been fulfilled, with further PPI cases to be managed through existing support centres.
"The lease on this Glasgow site expires in 2014. Having evaluated all the possible options, we made the decision not to negotiate a new lease."
It added that it was committed to working with staff affected by yesterday's decision and would possibly try to redeploy some of them. The Glasgow site is due to shut down in March when the building's lease expires.