Now, Met Police have arrested a 29-year-old man on suspicion of causing criminal damage.
Police also seized a motor vehicle and bailed the man to a date next month.
"This is a positive first step in this investigation, but it does not end here," Inspector Rob Bryan said in a statement.
"I reiterate my request for anyone with information about this crime to come forward.
"Someone knows the truth of how these gravestones came to be damaged and I urge them to speak up."
There are 120 World War I graves at Harefield Park (St Mary) Churchyard for mainly Australian troops who died at the nearby No 1 Australian Auxiliary Hospital.
Each grave is marked by scroll-shaped headstones, chosen by the staff and patients at the hospital.
One New Zealander is buried at the graveyard - Dunedin-born private John Duncan Fletcher who died while serving with the Australian Infantry's 57 Battalion.
The RSA this week condemned the desecration as a "wanton act of vandalism".
"Such an act is appalling and can never be justified in any way," said New Zealand Returned and Services Association chief David Moger.
"It is completely disrespectful to all those who gave their lives in service."
It is understood that the Commonwealth War Graves Commission is working on repairing the damage.
It is the second such incident this year. A memorial in the cemetery was sprayed with paint and the Australian flagpole cut into on the eve of the Gallipoli centenary.
