Hi Deb,
Details at this site... Scroll down to gravesearch enquiries.
http://www.fonc.org.uk/"Gravesearch enquiries can be made to Southwark Council who, at the time of writing, make a charge of £14 for each name that they search in the records. Payment must be in pounds sterling, Cheques should be made out to "London Borough of Southwark".
If you think that a relative might be buried in Nunhead Cemetery then please write in the first instance to:
The Superintendent of Cemeteries,
Camberwell New Cemetery,
Brenchley Gardens,
London,
SE23 3RB,
England
giving all details including the full name of the deceased and their date of death (searches will include two years either way). The cemetery staff will supply a grave number and a square number which will enable you to visit the cemetery and look for a gravestone."
They didn't use to charge. Seems a bit steep but no other way to do it really.