Around 28 graves, of Australian war dead, were graffitied with blue paint on Saturday night. The corner of one tombstone was completely broken off.
They're part of 112 graves which make up Britain's national Anzac cemetery in St Mary's parish churchyard in Harefield, West London.
The Commonwealth War Graves Commission has begun restoration work on the tombstones.
Police are still looking for the perpetrators, and it is unclear why the graves have been targeted on two seperate occasions. The first was the night before Anzac Day earlier this year.
Revd Martin Davies, vicar of St Mary's, told Premier: "We think that somebody does know who did it, and the simple answer would be for the person who knows to come forward and tell the police and then we can wrap it up and sort it out.
"We cannot have this sort of thing happening again. This has really hurt people quite seriously and its an affront to Australians.
"This is something Australia values very much, that we have this cemetery in this country and that we care for their war dead.
"It's more than the congregation [that's been affected], I mean the village owns this cemetery.
"In the First World War people were brought to what is now Harefield Hospital, so the association is with Harefield Hospital. It's with the village as well as the church, and the whole village feels deeply aggrieved that this sort of thing should happen.
Listen to Premier's Aaron James speaking to Revd Martin Davies here:
