Is this a burial date or a death date? What age was he when he died? If David died young then there is a strong possibility at least one of his parents will be named in the burial registers.

Civil Registration of deaths didn't begin until 1837.

It looks like Emneth parish registers have been microfilmed by Wisbech Museum. I often have the same 'problem' when searching for ancestors in the English Fenland, sometimes the only way of searching some records is to actually go to Wisbech (which isn't an option available to all of us)! I see you've visited Rootschat, they're a helpful bunch so maybe someone there can help. I work near the Society of Genealogists in London and I notice they have a microfilm copy of the records. I can't guarantee I'll have time to search it any time soon (microfilms are fiddly) but if I have a spare 10 mins maybe I'll take a look.

At least I've discovered Emneth is in Norfolk, not Cambridgeshire, so I've learnt something new!!