John Ryan, 53, an operative with the company, was stabbed repeatedly near his home in Guildford Road, Walthamstow, on the evening of 4 December. He died on 20 January in Whipps Cross hospital, 47 days after the attack.
Officers from the Metropolitan Police's murder investigation team began questioning Murphy staff this week in an attempt to uncover a motive for the murder.
A source close to the investigation told Building that the attack appeared to be an isolated incident.
He said Ryan had locked up his Murphy van close to his home when a man started talking to him. It is believed the conversation led to an argument at about 7.40pm.
The source said Ryan was then stabbed by the man, who then fled the scene, passing underneath a North Circular flyover.
It is understood Ryan was later found staggering in the street by his family and was taken to hospital.
The team will interview staff at Murphy to find a clue about the murderer
Source close to the investigation
The source said that the police seemed to have exhausted their first lines of inquiry and had turned their attention to interviewing Murphy staff.
The source added: "The investigation team will now begin to interview staff at Ryan's employer Murphy to try to find a clue as to the identity of the murderer."
A company source said Ryan had led a quiet life. He said Ryan was a "creature of habit" and that there was no apparent motive.
The source added that feelings were running "very high" over the murder and that there was a real determination to help the police catch the culprit.
He said: "John's funeral was only a couple of weeks ago so the incident is still fresh in people's minds. There is a real sadness in the air."
Murphy said it was helping the police with their inquiries.
Officers leading the murder hunt described the knifeman as a white man in his mid 20s with a blond ponytail. They have urged the public to come forward with any information to aid the investigation.