Interesting, I checked the Association English database.There are plenty of Henrys but none born circa 1836.
As you may know there were two ancient Churchill families in England.The most prominent was the family of the first Sir Winston circa 17th Century.They are called the Dorset Churchills (because that is where the family originated).They date from Normandy before the Conquest. Their English Progenitor was an Elias de Churchulle b. 1271.
The lesser known family is the Oxfordshire Churchills.Their Progenitor simply appears in OXON records in 1300.Their origin and how they came to use the Churchill name is unknown.
The two families are not at all related - although until the DNA Project it was thought that they were.Devon Churchills are of the genetic Haplogroup I-1a which makes them of Nordic origin.This is consistent with the 1st Sir Winston's written ancestry.
The OXON Churchills are in Haplogroup R-1b which makes them of middle European Origin from circa 13,000 or so years ago.
Individuals in I-1a and R-1b are not at all related.
The Association has the genetic signatures for Churchills of both families.I would recommend that you consider Y-DNA testing.From that, at minimum, you should learn to which ancient English family you belong.
Regards, Bill Churchill CHURCHILL Y-DNA Genesis Project.