The rocker and his wife, Polly Sampson, are currently working to improve their $4.8 million (£3 million) coastal mansion in Hove, England, and recently submitted a planning application to local authorities for permission to move a marble commemorative cross which is situated on the wall of an outbuilding.
Gilmour wants to re-position it so he can extend a storage room for his canoes.
The monument is dedicated to an army officer who died of typhoid fever in 1889, and local activists insist Gilmour shouldn't be allowed to displace the memorial.
Valerie Paynter of campaign group Save Hove tells Britain's Daily Telegraph newspaper, "It's not neighbourly: it's a middle finger to local history. From the very start they have showed utter contempt for that cross. They want to wilfully and selfishly hack into and damage local history - for a canoe."