During my searching, however, I discovered that his father John, had apparently emigrated to Kansas, USA, followed later by his wife and youngest daughter, Ellen, aka Nellie. I already knew that, in the 1871 census, Frances Perkins and Ellen were living with Frances's son, Frank in Kent, so some time between then and 1880, the two of them decamped to Kansas to join John. By then John and Frances were in their fifties, so it seems a big step for them to take at that stage of their lives.
Some of this information has been further supported by Charles' army papers, which Dad recently found again.
So, some of the mystery is solved but many questions still remain and probably will never be answered.
Why did Charles appear to change his middle name, which is Frederick on his baptism certificate, Ernest on his death certificate and doesn't appear at all on his marriage certificate or in his army papers?
Why does there appear to be no record of his birth?
Why did John and Frances decide to emigrate to America in their fifties?
Why did Charles fall out with most of his family, including, it seems, his parents? I have first hand information from Dad that he did and this seems to be backed up by the entry for 'parents' address' in his army book, where, having crossed out the earlier address at some time, he has replaced it with a box number in USA.
Maybe we need the services of a medium!