Maintaining graves and memorial stones is a big problem for local authorities, who I understand now get no support from central government, and have to raise all their finance from local rates. Different local authorities had different policies, according to the council members, officers, and the attitudes of the local population. Although I was never responsible for this kind of service, I sat for 15 years through six-weekly meetings of Lambeth Council, at which the ins and outs were discussed.
My feeling was that council officers had more feeling than the politicians had for the problem of neglected memorials, when at that time there was some central government support.
The real issue seemed to me to be that no-one had any interest in the vast majority of the memorials, and resented public money being spent on them.
The Lambeth compromise was to remove all the stones from the original site and place them around the edges of the cemetery, grassing over the site of the graves. Occasionally there were problems with individuals claiming an interest in a particular memorial, but there was rarely any willingness to pay for anything themselves.
Sorry if I sound hard - I write this with sympathy for the descendants and respect for the departed.
Peter