John Barrett attacked 50-year-old Denis Finnegan on 2 September 2004, stabbing him to death as he cycled through Richmond Park.
Barrett was being treated at Springfield Hospital in Tooting following psychotic symptoms including hallucinations. He had walked out the day before on authorised leave and failed to return.
He was convicted of manslaughter in February 2005 and an independent inquiry was ordered by then health secretary John Reid following calls by Mr Finnegan's family.
The report, published in December 2006, was highly critical of the forensic service management and of management in general at South West London and St George's Mental Health trust, and of the care Barrett received from psychiatrists.
Unusually, it made a single recommendation - that a service improvement team should work with the trust to identify failings and monitor progress.
The team suggested a number of improvements, some of which are still outstanding, such as an improved substance misuse model and medical staffing strategy.
The trust also undertook its own internal inquiry, which led to changes in leadership and improved training.
John Finnegan, Denis' brother, said the reason for the two-year delay was because the strategic health authority had waited too long before commissioning the independent inquiry.
'It took over two years after my brother was killed for the report to come out. It's a horrendous amount of time to wait.
'There's no reason why they couldn't start reporting on John Barrett the day he killed Denis. He pleaded guilty and there was no doubt in anybody's mind that there were any mitigating circumstances.
'I pestered them right from the beginning to sort the problem out straight away. If the police have got all the information they need, and he's admitted he's guilty, there's no reason why they couldn't have started the independent investigation.
'I think they wanted it to take two years so the sting had gone and people weren't as angry. They were letting it cool down instead of getting on with it straight away.'
A spokesman for South West London and St George's Mental Health trust said that the one recommendation in the independent report - to work with a service improvement team - had been implemented.
He added: 'There have been regular meetings with the Home Office (now Ministry of Justice), NHS London and Richmond and Twickenham primary care trust, who monitor progress against the report.'
NHS London, which has been monitoring the trust's progress since it took over responsibility last August, declined to comment.