O’Keefe, who denied murder, is due to be sentenced later today.
A spokesman for South London and Maudsley NHS Foundation Trust said O’Keefe’s escape "should not have happened" and apologised unreservedly.
He said: "We would like to offer our sincere condolences to all those affected by Mr David Kemp’s death.
"Terrence O’Keefe absconded from an acute hospital, where he had been taken for medical treatment, while under escort by our staff. It should not have happened - and we apologise for that unreservedly.
"Immediately after the incident, and since, we initiated major improvements and have strengthened the arrangements for transferring medium secure unit patients to acute hospital for treatment.
"Changes we have made include increasing the escort to as many as four staff per patient.
"Where necessary, we now use security guards who are authorised to apply handcuffs.
"We are also piloting the use of an electronic tracking system for the first time within the UK mental health system."
