Outsourcing firm Capita has announced plans to relocate around 350 jobs in Bristol to the company's sites in Darwen, Lancashire and Mumbai, India.
It is also expected that five jobs will be lost from the TV licensing site in Glasgow, while more than 40 management jobs from field operations will also be lost.
Staff were briefed today on the plans and the jobs are expected to go by September 2012.
The Communications Workers Union said that the move was "callous", adding that compulsory redundancies would affect Bristol "particularly heavily".
Andy Furey, the CWU national official, said that the BBC's deal in late 2010 to freeze the licence fee for six years is now having an impact "outside of the corporation".
"It appears that Capita has sacrificed the livelihoods of people in Bristol, Glasgow and elsewhere as cost-savings to win the BBC TV Licence contract, rather than finding legitimate savings elsewhere," he said.
"Hot on the heels of the move to Salford, the BBC licence fee freeze agreed by Mark Thompson is now responsible for job losses outside of the corporation. This is the reality of that decision - unemployment. It's irresponsible and unfair."
Only last month Capita was awarded a new contract by the BBC to administer the £142.50 TV licence fee for an eight-year term starting in July, worth approximately £560m.
The deal followed a series of strikes by the CWU at Capita's TV Licensing sites over a dispute about pay.
Furey added: "Capita management seem to be punishing staff in Bristol and Glasgow who have fought hard for a decent pay rise in recent months. By cutting these jobs they lose experienced and dedicated staff which can't be good for business continuity.
"We will be working closely with our members over the coming weeks to see how jobs can be protected and what options are open to them. We're completely shocked by Capita's callous attitude towards long-standing employees and see this as a direct attack on union rights. We will work hard to ensure union representation is retained in this giant company."