National Savings is to transfer some of its operation to India, it has emerged.
Versions of Ernie have been in use since 1957 when the bonds began
The government-owned Premium Bonds company contracts some of its work to Siemens, which is in turn moving some of its administrative jobs to India.
National Savings says no jobs are at risk at the Premium Bonds headquarters in Blackpool, but unions are concerned about job security.
The news comes as National Savings launches a new version of Ernie, the computer which picks bonds winners.
Siemens won a Private Public Partnership - the forerunner to the private finance initiative - contract with National Savings in 1999, and 1,000 jobs were transferred to Siemens.
The firm is now to have its contract extended by a further five years.
The Public and Commercial Services Union (PCS) says staff in Blackpool are concerned the operation is being broken up for commercial reasons.
PCS branch secretary Duncan Wilding said: "If the plan to offshore jobs goes ahead hundreds of PCS members will feel betrayed.
"There is no benefit for the UK government, the taxpayer or National Savings customers in this proposal.
"It is purely aimed at saving the private contractors millions of pounds.
"The UK government must set an example to UK industry and must reject offshoring government work."
A National Savings spokesman told BBC News Online that it was "routine administrative tasks" and not actual jobs that were being moved.
"It is not about shunting British jobs to India," he added.
He said the move allowed Siemens and National Savings to offer new and expanded services in a cost-efficient way, with better opportunities for Blackpool workers.
Meanwhile Ernie 4, the new Premium Bonds number generator, is being unveiled at the Science Museum in London on Friday.
Ernie - an acronym standing for "electronic random number indicator equipment" - has been central to the whole concept of Premium Bonds since their inception in 1957.
Ernie produces a vast number of random numbers during each draw, which represent individual premium bonds. Premium Bonds prizes range from £50 to £1m.
The new Ernie is able to produce one million winning numbers an hour, which is three times faster than its previous incarnation.
The odds against winning a prize on the Premium Bonds is 24,000-1.