No, it won't have his place of birth on his death certificate -- that wasn't introduce untill (i think) the 1960's
You could contact the local Register Office with the details that you know (last known address, occupation, wife) and see if one of the certificates match those details.
(Thos this isn't foolproof -- i recently did this and got told they couldnt find the certificate -which turned out to be because the son-in-law who gave the information gave the wrong forename for his MIL's husband who had died some 40 yrs earlier)
As for being buried in the parish churchyard -- that would depend on how big a graveyard it has -- if only a small graveyard it could be full and burials take place at the municipal cemetary some miles away. Or, particularly in Wales, there could be a number of small Chapels in the area that might have graveyards