There's no central record.
You've not stated how long ago the person died or how much other information you have. If the death occurred in fairly recent years, and the deceased person left a will, their executors will probably be able to give you the information you require. The will is a public document and it will name the executors (probably also giving their addresses). You can get a copy of the will from the Probate Registry:
http://www.hmcourts-s...e.gov.uk/cms/1226.htm
Again, if the death was fairly recent (and you know where in the country the person died), phoning around local funeral directors might yield the relevant information. (Use Yell.com to find the phone numbers).
Similarly, looking through the 'death' columns in the archives of local newspapers might help. (Contact the main reference library for the area, or the county records office).
If the death occurred many years ago, you're probably limited to checking church records and similar documents.
Remember, of course, that (in the case of cremation) many people don't have their ashes 'laid to rest' anywhere. They may simply have been scattered somewhere that a relative (or whoever arranged the funeral) thought to be appropriate. (My own will asks that my body be cremated without ceremony and that my ashes be disposed of, also without ceremony, in any convenient refuse receptacle. I used to prepare wills for a living and I know that my wishes are by no means unusual).
Chris