An investigation was launched after police were called to Exeter House on Watermill Way at 11.08pm on Friday, 21 June to reports of a shooting.
Armed police, local officers, London’s Air Ambulance and the London Ambulance Service attended and found a man injured.
Despite the efforts of paramedics a 25-year-old man died at the scene a short time later.
Formal identification will take place in due course but detectives have previously named the victim as Edward Simpson of Feltham.
A special post-mortem examination took place at Fulham Mortuary on Sunday, 23 June and gave the provisional cause of death as a single gunshot wound to the upper body.
Edward’s next of kin continue to be supported by specially trained officers.
A 27-year-old man was arrested on Monday, 24 June on suspicion of murder and has been released on bail to return on a date in late July.
On Tuesday, 25 June two other men – aged 26 and aged 22 – were arrested on suspicion of murder.
They have been released from custody and bailed to return on dates in July.
A 24–year-old man was arrested on suspicion of harbouring an offender and has been released under investigation.
These arrests follow enquiries by detectives from the Homicide and Major Crime Command.
Detective Chief Inspector Katherine Goodwin is leading the investigation.
“We are still working hard to identify who is responsible for this horrendous and callous crime and bring those responsible to justice. We have made a number of arrests, but still have some way to go in achieving justice for Edward’s family and friends.
“We believe a number of people were in the area at the time but have not felt confident enough to come forwards with vital information. We would like to speak with anyone who saw anything on the night or has knowledge around who was responsible for the shooting.
“Your information could save lives.”
Anyone with information is asked to call the incident room on 020 8785 8244 or via 101, quoting reference CAD 9535/21June.