Darlington Borough Council has come under renewed attack over the security at the town's West Cemetery.
The authority admitted earlier this year that the cemetery gates were no longer locked at night, leading to criticism from people whose relatives are buried there.
One woman, whose mother and mother-in-law's ashes are buried at the cemetery, has offered to lock the gates herself.
The woman, who does not wish to named, said: "I think it is appalling that the council can do this.
"It is such a beautiful cemetery, and it is obvious that it is going to be hit by vandals if it is going to be left open at night.
"How much can it cost for someone to go down there and lock the gates?
"If no-one can do it I would be quite willing to do it myself."
Darlington council took the decision to leave its cemeteries unlocked in July, and introduced 24-hour mobile patrols to replace park-keepers.
The authority says the wardens are better equipped to deal with incidents of vandalism because they are linked directly to the police.
Council spokesman Steve Jones said: "We like to think of it as a different way of delivering a better service.
"We don't physically have the staff to lock all the gates to our parks and cemeteries.
"And if anybody is hell-bent on thieving and vandalism, it is almost impossible to stop them getting in anyway just by locking the gates.
"The wardens will ask local residents if they are having any problems and will be able to respond quickly if there is anything going on."
Comments: Our rules
We want our comments to be a lively and valuable part of our community - a place where readers can debate and engage with the most important local issues. The ability to comment on our stories is a privilege, not a right, however, and that privilege may be withdrawn if it is abused or misused.
Please report any comments that break our rules.
Read the rules hereComments are closed on this article