RBS and Lloyds have announced they will cut 1,900 jobs between them, whilst Jaguar Land Rover has created 1,000.
Lloyds, 40 per cent owned by the taxpayer, is cutting 1,600 jobs. The bank plans to halve its international presence, and this move is one of the first steps towards that.
RBS, which is more than 80 per cent owned by the taxpayer, is cutting 460 jobs and creating 150 elsewhere, leaving it with a net loss of 300 posts.
The government bailed out both banks in 2008.
The job losses at RBS will be from its private banking operations. The company said: "We are working hard to rebuild RBS in order to repay taxpayers for their support and having to cut jobs is the most difficult part of this process."
David Fleming, Unite national officer, told the Telegraph:
"To learn that 300 jobs are being transferred to a low wage economy adds insult to injury. Once more these banks are attacking some of their lowest paid staff to achieve cost savings."
The Unite trade union asked why the Government was not intervening. Both banks said they would try to keep compulsory redundancies at a minimum.
Meanwhile, Jaguar Land Rover will create 1,000 jobs at its factory in Merseyside.
The workforce at Halewood will expand to almost 4,500 – treble the number from three years ago. The company said the new jobs are a response to "significant demand" for some of its models.
It is the second jobs boost in a week in the motor industry after Japanese car giant Nissan announced plans to build a new model in the UK under a £125m investment programme, creating 2,000 jobs.