An inquiry has been ordered by John Reid into the killing of a cyclist by a paranoid schizophrenic a day after he walked out of a mental hospital.
Barrett had a history of violence when he killed Dennis Finnegan
The health secretary said the stabbing of Denis Finnegan in September 2004 by John Barrett, in Richmond Park, south-west London, raised questions.
Barrett, 42 - who has a history of mental health problems - pleaded guilty to the banker's manslaughter on Friday.
Dr Reid said there were implications at both local and national levels.
"I have asked for a report to be compiled. I want the local strategic health authority to carry out an independent inquiry," he told the BBC.
"But not only into the local implications but some of the national implications of this.
"I think that on face value there are some very difficult questions that have to be asked about this."
Despite a long history of mental illness and violence, Barrett had been given "ground leave" from Springfield Hospital in Tooting, south London.
Doctors had no power to keep him against his will and he was allowed to wander the hospital complex unescorted on the understanding that he would return to the clinic.
Instead he walked out and the following day, 2 September, stabbed Mr Finnegan to death as he cycled through Richmond Park.
South West London and St George's Mental Health NHS Trust, which runs Springfield Hospital, is already conducting an internal inquiry into the circumstances surrounding the case.
The inquiry follows calls by 50-year-old Mr Finnegan's family for such a move.
After Barrett's guilty plea Mr Finnegan's brother John said the family were "devastated" and that "everybody involved in his care should be ashamed of themselves".
"As you can imagine, losing a brother in such circumstances is diabolical.
"And to say it could have been prevented makes it worse."
Barrett is to be sentenced 22 March.