Hounslow police have upped their patrols of the area around Bedfont Cemetery following the apparent theft of a gravestone.
The Chronicle reported last week how the family of a former air force sergeant John Moriarty were left devastated after his headstone and other parts of his grave went missing.
Det Con Emma Phillips, of Hounslow CID, this week admitted to the Chronicle: "From a police point of view there's nothing we can do about it at the moment. There's no forensics, CCTV, or witnesses, and it could've taken place anytime since the last visit four or five weeks before.
"But local safer neighbourhood team officers are aware of the situation and patrols are being increased in the area."
Mr Moriarty's family called for improved security after council cemeteries chiefs admitted the gates, which are often left open, are not locked by staff for financial reasons.
Anyone with information can call Hounslow CID on 020 8247 6271 or Crimestoppers anonymously on 0800 555111.
