Dear Mr. Burke,
Thank you for posting on History Hub!
The National Archives does not have information on local family-owned cemeteries.
A family cemetery generally consists of burials for persons related by blood, marriage, or household. It is possible that the persons buried in the cemetery were servants, distant relatives, friends, etc.
Ultimately, research would need to be conducted on each individual buried in the cemetery to try to determine their relation to the family, if any.
We suggest you look at census records for the location or for the family. Census records often mentioned all members in a household including servants, guests, boarders, etc.
We also suggest you look at local newspapers. Newspapers may mention a person's death or burial and may provide clues as to why the person was buried in that particular cemetery.
We hope this information aids you in your research!