Plans to electronically send records of UK births, deaths and marriages to India for indexing are "outrageous", a civil service union says.
The UK has seen a recent surge of interest in genealogy
The PCS said the Office of National Statistics was playing "fast and loose" with sensitive information and that hundreds of UK jobs could be lost.
About 250 million records from England and Wales dating back to 1837 would be encrypted before being sent to India.
The ONS said the move would help people to trace their family histories.
It says the project, which would take about three years to complete, would be secure and would lead to a more efficient online service.
The ONS is in talks with engineering giant Siemens, the preferred bidder, to take on the work.
"These are important records charting the births, deaths and marriages of this country's population which should be maintained securely in the UK public sector by people accountable to us all," said Mark Serwotka, general secretary of the PCS union.
He called for ministers to intervene, to ensure "that the population's personal information remains in the public sector".
As well as attracting criticism from the PCS, the proposal has led to a cross-party Early Day Motion.
The records are currently held in Southport, but would be sent to Chennai, creating around 1,000 jobs.
The UK has seen a recent surge of interest in genealogy - the research of family history.
Last year, BBC Two's Who Do You Think You Are? programme, which followed celebrities as they traced their family tree, was credited with inspiring viewers to find out more about their family history.
The advent of old paper records being made available on the internet has made this much easier.