Alan Wardle kindly sent me details of the following website. Thanks Alan!

Fareham Borough Council have a free searchable online database that covers all eight of the cemeteries in it’s care. You can search by surname, cemetery or plot number and once the right entry has been found the details given include full name, cemetery, plot number. A search just on the plot number of a certain cemetery gives the details of all those buried in that plot.

Very helpful site, wish I have ancestors from this area!

http://www.fareham.gov.uk/bereavement/funerals_and_burials/burial_search_facility/cemrecsearch.asp