Norwich Union Life says it has no plans in the pipeline for any more significant job losses in York, following yesterday's announcement that 150 posts are being axed.
But a spokesman has stressed that the company must remain efficient in a competitive market, and look at more ways of being even more efficient.
"A good efficient company is good for the majority of staff and good for the future," he said.
Asked if that meant jobs could not be guaranteed, he said: "I don't think anyone gives guarantees nowadays."
Norwich Union, which employs a total of about 3,500 people at various sites across the city, is cutting 700 jobs across the country, including 150 in York.
Another 250 people working under contract across the country are also set to lose their work, although it is not known how many of these jobs will go in York.
The work in the life business services division, mostly software development and application support, is being transferred to outsourcing companies operating globally, in locations including India.
The move comes after the company announced earlier this year that the work of about 25 employees in the IT departments was being switched to India, although the local staff were all being found other jobs.
The company has confirmed that IT experts from India have been working alongside York employees in the city in recent months, in preparation for the transfer of the work, but this did not pose any problem for local workers.
An Amicus official said that the union will meet Norwich Union bosses today for the first informal talks since the latest jobs culls.
She restated Amicus's "vigorous opposition" to compulsory redundancies and said the company employed enough people for retraining and relocation to be considered.
During the talks, the union would be asking how many of the latest jobs lost would go abroad or be outsourced in the UK.
Vale of York MP Ann McIntosh said she had been in contact with senior management over the job losses, and would work with organisations such as the Learning and Skills Council to help find alternative employment for workers as quickly as possible.
Updated: 10:15 Friday, June 11, 2004
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