But no evidence could be found and the new owner is unwilling to give up the plot.
The council says it made extensive efforts to research the Kenealy name but could not find any descendants. That mystifies Mr Davis, who says the Kenealy plot has long been a sacred place for family members to visit, pray and reflect on life.
Reserves and Facilities Officer Sue Hammond wrote to Mr Davis apologising for the way in which he had discovered alterations to the site. Council's records had shown the plot beside his grandparents' one was vacant, and the "full and exclusive right of burial" had been reserved and sold some years ago, she said.
When the new owner asked for the concrete to be removed, the council researched the Kenealys.
Under the Burial and Cremation Act 1964, the council is entitled to sell the right of burial in any part of a cemetery as long as a plot had remained unused for 60 years, said Reserves and Facilities Manager Peter Watson said.
"On this basis, the plot next to your grandparents was available for purchase by the public, with ... the plot having subsequently been sold in May 2003 ... "
Mr Davis said he and other descendants were appalled at what he claims amounts to desecration of family graves.
Mr Davis said his experience should sound a warning to residents whose ancestors are buried in the old cemetery: "We would never have thought that the council could do something like this, but they can."
In a letter to Mr Davis, Mr Watson said the council was satisfied it made reasonable attempts to find the family, including consulting an historian.