Hi
You will need to approach each council area's burial authority.
For Swansea it will cost you 5 pounds for them to search the Municipal cemeteries.
http://www.swansea.gov.uk/media/word/6/f/Search_application_form.docTheir contact details are on their above website that Dawnsh posted if you want talk to them via phone or email them.
It was a free service a few years ago, I suppose they have to charge now with so many people trying to find where their ancestors are buried
If it were me I'd give them a phone , and explain about your father's wish to find his g grandparents graves
because of his mother's ashes- they may look to see if they are in one of the municipal cemeteries for you with no charge ( we were never charged just a few years ago for my hubby's g grandmother - I'm very surprised they seem to charge now as they have always been very much approachable, and helpful)
The nearest thing to a national database for UK is deceased online - which is a very, very long, long way off from being completed ,it's still very much in it's infancy
http://local.direct.gov.uk/LDGRedirect/index.jsp?LGSL=335&LGIL=8&ServiceName=Find out about burial and grave details
If you mean is there a database listing all cemeteries in England and Wales - no, there is apparently a lack of information on how many cemeteries is in existence (operating and closed ones) this is interesting reading:
http://webarchive.nationalarchives.gov.uk/20110118095356/http:/www.cabe.org.uk/files/cemeteries-churchyards-and-burial-grounds.pdf It seems you have a lot of searching to do , they could be buried anywhere from Wales to Guernsey - Has your father got any first cousins who are still alive that are in the UK, or children of his cousins - if he has maybe contacting them may be fruitful in finding where they are buried.
Hope that helps
Kind regards