National Australia Bank (NAB) also warned of possible branch closures as it looks to save up to £117 million a year at the Clydesdale and Yorkshire.
Most of the restructuring will involve back office jobs, after NAB confirmed it wanted to strip out the duplication of posts among the two businesses, which have been run as separate entities and employ a total of 10,300 staff.
Glasgow-based Clydesdale dates back to 1838 and has 217 branches, while Yorkshire, founded in 1859 in Halifax, has 232 sites, run from Leeds. The company, which acquired the businesses in the late 1980s, has not detailed where the jobs will go or which “unprofitable” branches could be axed.
Union representatives from Amicus pressed bosses to rule out compulsory redundancies and avoid any “last bank in town” branch closures. The jobs will be lost within 18 months, but could be offset by redeployment and normal turnover.
The Australian bank carried out a review of its British arm after offloading its Irish business - Northern and National Irish Bank - earlier this year.
The group had been seen as a potential buyer of Abbey National but is now focused on driving growth in Britain through its two existing brands.
It has identified Britain as “an attractive market with a positive outlook”, but said its operations lacked a structure and distribution network to take advantage.
NAB’s British chief executive Lynne Peacock said: “We have completed the sale of our Irish operations, and are now concentrating on ensuring our UK businesses are more nimble and customer-focused.
“We have made it clear that we are committed to a strong presence in the UK, but to do so we must change the way we do business.”
NAB has most of its operations in Scotland and the north of England but recently began an attack on the south-east of England by opening 15 Clydesdale-branded centres for use by small and medium-sized businesses.
A further 15 will open in the region by the end of the year while NAB wants 50 “flagship” centres focused on personal and business banking elsewhere.
Among other changes, NAB said it would simplify its range of products - down from 320 across both banks to 140 - and look to develop telephone and internet banking. It said there were no plans to merge the operations.