Calls to put the DNA of every UK resident on a national database are impractical, the government has said.
Both killers were convicted with compelling DNA evidence
A senior police officer has argued for a universal register, after two killers were convicted on DNA evidence.
Sally Anne Bowman's killer, Mark Dixie, and Suffolk serial murderer Steve Wright were both captured because their DNA was taken after unrelated offences.
But the Home Office said a mandatory database "would raise significant practical and ethical issues".
The DNA database, which covers England and Wales, currently contains around 4.5m profiles - routinely taken from criminal suspects after most arrests.
It is already the largest of its kind in the world but is controversial.
Since 2004, the data of everyone arrested for a recordable offence - all but the most minor offences - has remained on the system regardless of their age, the seriousness of their alleged offence, and whether or not they were prosecuted.
'Reasonable and proportionate'
Steve Wright was on the system after being convicted of theft in 2003, and when police found his DNA on the bodies of some of his victims they matched it with his profile.
But Mark Dixie was not on the system at the time of Sally Anne Bowman's murder in 2005.
It was only when Dixie was arrested for assault after a fight in a bar that his DNA was taken and he was linked to the murder.
He was arrested within five hours.
Det Supt Stuart Cundy, who led the murder hunt which led to Dixie's conviction, said: "It is my opinion that a national DNA register - with all its appropriate safeguards - could have identified Sally Anne's murderer within 24 hours.
"Instead it took nearly nine months before Mark Dixie was identified, and almost two-and-a-half years for justice to be done."
The Association of Chief Police Officers (Acpo) is also calling for a debate on the issue.
Lincolnshire's Chief Constable, Tony Lake, who speaks for the association on DNA, said he was not convinced by the need for a universal database, but recognised the arguments on both sides.
He said: "If there was a national database of everybody then we would solve more crime, of that there is absolutely no doubt...
"But any database that we hold has to be reasonable and proportionate in the eyes of the public."
No 'silver bullet'
Home Office minister Tony McNulty said a national database was not a "silver bullet" and it would raise practical as well as civil liberties issues.
The proposal is for all DNA samples to be kept on police databases
"How to maintain the security of a database with 4.5m people on it is one thing," he said.
"Doing that for 60m people is another."
Shadow home secretary David Davis said the debate about a DNA database should be put on a "statutory footing".
"Only then can we address anomalies like the fact that database contains details of hundreds of thousands of innocent people...
"But does not hold the details of every serious offender."
The Liberal Democrats said the party was opposed to the idea of a national system saying it did not "stack up on practical grounds".
Home affairs spokesman Chris Huhne told the BBC it would involve "a massive intrusion into civil liberties".
He said there would be "a real question mark over potential abuse if DNA samples and details were lost".
In September 2007, Lord Justice Sedley - one of England's most experienced appeal court judges - called for the register to be made universal.
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 condemned the existing system as "indefensible", said it was biased against ethnic minorities, and it would be fairer to include everyone, guilty or innocent.
Human rights organisation Liberty said a universal database could be open to abuse.
But law reform group Justice said a national database should either list those guilty of a crime or everybody in the country.
Meanwhile, the existing register could be threatened when the European Court of Human Rights is asked to rule next week on a test case of two Britons who want their details removed from the database.
The pair, from Sheffield, had their DNA taken after they were arrested in 2001, but charges were not pressed.
The applicants say their human rights have been infringed by the decision to leave their details on the database, despite the fact that they had never been found guilty of a crime.