The Lloyds TSB Group Union (LTU) has been arguing for some time that jobs that have been transferred to India over the past five years should be returned to the UK.
"As part of our negotiations on the takeover, the union will be insisting that to help mitigate large scale job losses in the UK, as the new combined bank seeks to remove overlaps and duplication - saving £1bn by 2011 - the bank should agree to immediately freeze all ongoing programmes that involve transferring yet more jobs to India," said the LTU.
Its call covers IT and back office function jobs. The LTU also wants the bank to "commence plans to return to the UK the estimated 3,000 jobs that have already been transferred to India, in order to safeguard existing UK jobs that would otherwise be lost as Lloyds TSB and HBOS operations merge together," it said.
In March, Lloyds TSB closed its call centre in Mumbai and returned the jobs to the UK.
Steve Tatlow, LTU assistant general secretary, said, "If the new bank is to be so dominant in the UK, it is imperative that it commits itself to supporting UK customers only from the UK.
"By ditching its 'jobs to India' strategy, the Lloyds TSB board would be shouting loud and clear that it genuinely is committed to the wellbeing of its customers, staff and the UK economy."