"Will people at birth get their genome sequenced? I have absolutely no doubt that at some point in the future that will happen, but not in the foreseeable future," he said.
The cost of mapping an individual's whole genome, known as sequencing, was coming down so fast that he said it would soon be cheaper to do that rather than test for specific genetic anomalies.
He believed predictions that it would soon cost just $1,000 (£650) adding that it could soon fall to "practically nothing".
However, even if that becomes the case, the cost of building what the strategy group termed a "central repository for storing genomic and genetic data" could be considerable.
The Government recently pulled the £12 billion National Programme for IT, at its heart a project to computerise everybody's medical records, after Andrew Lansley, the Health Secretary, said it "wasted taxpayers' money".
Dame Sally Davies, the Chief Medical Officer for England, also a member of the group, said yesterday that it was likely the database would grow bit-by-bit, starting with the results of those who needed specific genetic tests.
The database idea is one a series recommendations made in the report, Building on our inheritance, Genomic technology in healthcare.
Mr Lansley welcomed the report, saying the promise of genomics was "immense". He also announced a new process for commissioning and funding genetic cancer tests, to ensure patients got the right drugs, to be in place by next April.
However, some experts believe the report hypes how the NHS is using genetic testing at the moment, and what can be achieved.
Dr Stuart Hogarth, a political economist at King's College London with a specialist interest in molecular diagnostics, said: "This report grossly exaggerates the current utility of testing for risk of common, complex diseases.
"For the most part, at the moment we can do no more than tell people that they are at slightly higher than average risk or slightly lower than average risk."
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