Concerns were raised this week after 20 headstones were found tipped over at Queensferry Cemetery.
Initially, it was thought vandals may have been at work.
However, the Gazette discovered that the City Council had moved the gravestones for safety reasons.
It has a policy that, if any headstone is in danger of falling over, it lays them flat.
While local councillor Norman Work defended the policy – to ensure that no-one gets injured or can sue – he was concerned that the council did not make any attempt to forewarn local elected members.
They could have then informed residents in advance, either online or on social media sites, to allay any fears.
The SNP councillor said: “I am concerned that I was not notified in advance of the action being taken.
“While I understand it would be difficult to contact all the families involved, it is equally distressing and disturbing for families to turn up at the cemetery to find that their family headstone has been laid flat.”