Unite expressed "fury" at the latest cuts, adding that a quarter of Lloyds' workforce has now been cut since 2009.
Lloyds Banking Group is to axe more than 940 jobs, bringing job loss announcements to 1,300 in the past few days, according to unions.
The Accord union said almost 200 posts were being moved offshore to India. Unions said it was the third job loss announcement from Lloyds in the past few days.
Unite national officer Dominic Hook said: "Since 2009 Lloyds have slashed a quarter of the workforce. It is a complete disgrace that the bank, which is 41%-owned by the taxpayer, continues to cut jobs in such a cavalier manner. In the middle of an economic crisis, a bank part-owned by the public should be keeping jobs in the UK, not exporting them abroad.
"Unite has warned Lloyds Banking Group that if they are looking for a period of stability and growth to return it to profitability, this cannot and will not be achieved by continuous and damaging job loss announcements. Unite opposes these cuts and will be doing everything possible to stop compulsory redundancies."
Lloyds said in a statement: "Lloyds Banking Group is today announcing 940 role reductions within the group operations, insurance, retail, wealth and international and commercial divisions. These form part of the reductions previously announced in the group's strategic review.
"Lloyds Banking Group is committed to working through these changes with employees in a careful and sensitive way. All affected employees have been briefed by their line manager today. The group's recognised unions, Accord, Unite and LTU, were consulted prior to this announcement and will continue to be consulted
"The group's policy is always to use natural turnover and to redeploy people wherever possible to retain their expertise and knowledge within the group. Where it is necessary for employees to leave the company, it will look to achieve this by offering voluntary redundancy. Compulsory redundancies will always be a last resort. In fact, during 2009 and 2010, slightly less than 50% of the role reductions made as part of integration have led to people leaving the group through redundancy."
Ged Nichols, general secretary of Accord, said: "This is a bleak start to the year for hard-working employees and is bad news for the UK economy on a day when the small fall in the numbers unemployed was supposed to be good news. The fact that nearly 200 of the jobs are to be outsourced to India is particularly unwelcome. Accord is certain that this is not what UK taxpayers would want from a bank in which they are the largest shareholder. Accord believes that Lloyds Banking Group (LBG) executives have a duty to think of the public interest before they offshore any more jobs."
Unite said Lloyds has cut more than 31,000 jobs since its creation in 2009, pointing out that on Monday the bank announced it was cutting nearly 200 human resources jobs and last week the company cut a further 175 jobs in the Halifax branch network.
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