Dear Jon
Burngreave Cemetery and parts of the General Cemetery are maintained by Bereavement Services (16 altogether). Although they do as much as they can, they say that it is the grave owner or relatives (and friends) to keep the grave tidy and would be very happy for you to do the "gardening".
We do some too while searching for plots for people who cannot visit themselves. Dave Yates is an expert! Christine. Friends of Burngreave Cemetery.