I wrote my response and hit the wrong key so I believe I lost my message.
My William Jarman does not appear to be as early as yours. He is my gggrandfather born in 1857 and died in 1912. He married Louisa Turtill who was a shoemaker's daughter in London, so he was in the London area to meet and marry her. They had 6 children some born in England and some in the United States as they used to travel back and forth. I have not heard of Elizabeth or Henry. The only information I have on William's father is his initials from a business card - A.J. Jarman - carriage makers.
But the crest is the same, so who knows, maybe we will find some comon connection at some time.