A group of eminent lawyers and scientists is calling for anyone not convicted of a crime to have their details wiped from the DNA database.
Former PM Tony Blair gives a DNA sample in 1999
The Nuffield Council on Bioethics said it is "unjustified" to keep people on the National DNA Database when they have not been convicted of any offence.
Some four million DNA samples are on the police's database.
Earlier this month a leading judge called for the whole of the population to be placed on the database.
In its report, the Nuffield Council warned that, while the national DNA database was an "increasingly valuable" crime-fighting tool, there needed to be a rethink on which genetic fingerprints are stored.
WHO'S ON THE DATABASE?
5.2% of UK population
Nearly 40% of black men
13% of Asian men
9% of white men
Source: Home Office and Census
The police can currently store DNA samples from anyone arrested in England or Wales for a recordable offence which typically can lead to jail.
A DNA sample remains indefinitely on the database even if someone is subsequently released.
That situation should be changed so that police should only keep the DNA of convicted criminals, said Professor Sir Bob Hepple QC, chairman of the body.
"Innocent people are concerned about how their DNA might be used in future if it is kept on the National DNA Database without their consent," said Professor Hepple.
Database: UK system largest in the world
"We would like to see the police put more resources into the collection of DNA from crime scenes, rather than from individuals suspected of minor offences."
The body said the only exception to this tightening of rules should be suspects of serious violent or sexual offences.
The experts questioned policies over "familial searching", where the DNA database finds partial matches because a relative is on the system, and attempts to identify ethnicity.
People who volunteer their DNA for elimination purposes, such as victims or witnesses, should have the right to ask for the DNA to be removed, said the council.
The council also called for greater support for juries hearing DNA evidence.
Earlier in September Lord Justice Sedley, one of the country's most senior judges, said the whole population and every UK visitor should be added to the national DNA database.
Deoxyribonucleic acid (DNA) is found in virtually all cells
Only a tiny sample of saliva, blood, semen, etc, is needed for testing
At the molecule's core is a long sequence of chemical units, which is checked for a gender and 10 other 'markers'
Probability of a chance match is less than one in one billion
A match may be with a specific individual or hint at a relative
Profiles can provide indications of ethnic origin
They do not point to genetic disorders or susceptibilities
He said the current system was indefensible and biased against ethnic minorities - and it would be fairer to include everyone, guilty or innocent.
But Nuffield said recording the DNA of the entire population would cost an estimated £700m - and this would be disproportionate compared with the potential benefit to society.
Currently each sample costs £4.50 to store for the first five years.
A spokeswoman for the Home Office said there were no plans to create a universal compulsory database - and there was clear evidence the database's rules were justified.
Of the 200,000 samples from people neither charged nor convicted, which would have in the past been removed, the spokeswoman said 8,500 had been subsequently matched to crime scenes, involving some 14,000 offences including 114 murders, 55 attempted murders and 116 rapes.
"Inclusion does not signify a criminal record and there is no personal cost or material disadvantage to the individual simply by being on it," she said.