Hi
People who have died after the 1950's, if not in the local churchyard, are most probably buried in municipal cemeteries, a list here
http://www.elmbridge.gov.uk/cemeteries/information.htmor more recently, likely to be cremated, a list of crematoria here
http://www.elmbridge.gov.uk/cemeteries/Cremation.htmLooking at the list in your first post, I would suggest you only have the entry from the death index, not the actual dates of death.
The first 2 questions the municipal authorities will ask will be the name and then date of death. Some of them will say they are too busy to search if you don't have the exact dates of death as they have too many entries to look through for every 3 months of the quarter in the death index.
Hope this helps.
Dawn