Hi, looking at the death index it looks like your father died in the Leeds area. Is that right, and if so do you know where he lived at the time? This might help work out where he was buried - there is a list of local cemeteries on the Leeds City Council website and ways to find check, if there is a location in mind.
Because he was quite young, you won't find much information on family history websites but as you know his name and date of birth, you could order his birth certificate (and marriage certificate if he was married), either from the office where it was registered or online from the General Register Office website. His birth certifcate will tell you his parents names if you don't know them.
I hope this helps - you could also have a look in local newpapers which are normally kept at the local libraries.