Officers were called to Exeter House, Watermill Way, Feltham at shortly after 11pm on Friday, 21 June, to reports of a shooting.
Armed police, local officers, London’s Air Ambulance and London Ambulance Service attended and found a man, believed to be aged in his 20s, critically injured.
The man died at the scene a short while later.
His next of kin have been informed.
A post-mortem examination will be held in due course as police are continuing with formally identifying the victim.
A crime scene remains at the location and police say that there are no other reported injuries.
This investigation will be led by detectives from the Homicide and Major Crime Command.
No arrests have been made at this stage with enquiries now being made to determine the full circumstances of the tragic incident.
Anyone with information is asked to call police on 101, quoting reference 9535/june21.
Alternatively, you can contact Crimestoppers anonymously on 0800 555 111 or online via https://crimestoppers-uk.org/give-information
Young people with information about violence or crime can visit www.fearless.org where they can pass on information anonymously. Fearless is part of the Crimestoppers charity, and is also independent of the police.