The move by the company is the latest in a rush of firms replacing local employees with well-educated but lower-paid counterparts on the subcontinent.
The bulk of the change will come at Aviva's Norwich Union arm, which already employs 1200 people in India and will add another 2350 by the end of 2004, moving call answering, administration and computing jobs from Britain.
The posts will be created in Delhi, Bangalore and Pune, Aviva said in a statement in London.
While some of the jobs would be new, others would be lost in Britain through turnover of staff and voluntary job losses, and Aviva said it did not rule out compulsory redundancies.
Trade unions representing British staff said the announcement was "deplorable", and accused Aviva of giving its British staff the "wonderful Christmas present of an uncertain future."
"This deplorable announcement by Aviva is based purely on greed," said Dave Fleming, a national officer with the Amicus union.
"Our customers want value for money products and high levels of service"
chief executive, Aviva
"It ignores Aviva's corporate social responsibility towards its UK employees and customers, because company turnover is overwhelmingly UK-based," he said.
He added: "They are throwing thousands of families on to the scrap heap for a 40% saving that will not be passed on to their customers."
However, Aviva which employs 59,000 staff worldwide - 33,000 of them in Britain - defended the move as a necessary measure in "an increasingly competitive environment".
"Our customers want value for money products and high levels of service so it is vital that we continually explore opportunities to improve our efficiency while maintaining service levels," said chief executive Richard Harvey.
"Making decisions that will affect our staff is always tough, but by taking action to remain competitive we will secure a long-term future for our business and therefore the majority of our people," Harvey said.
British trade unions warned recently that up to 200,000 jobs could be lost as companies transferred operations, principally telephone call centres, to India.
Indian university graduates, whose often impeccable English is a legacy of Britain's rule over the subcontinent, can be employed in call centres for around a fifth of the wages given to their English counterparts.