Hello Patricia
I believe I am probably related to the Henry family you describe. I have an Alexander Henry (1788-1865) on my family tree - I share autosomal DNA with two of his decendants.
The 1851 England census shows "my Alexander" as residing in the civil parish of Birtley, in the ecclesiatical parish of Chester-le-Street, County Durham. The record shows that his wife's name was Maria. His children James Henry (age 19) and Margaret Henry M Clennel (sic) lived at the same address. Margaret's married name was actually McClelland. James later married Bridget Cairns.
They all moved a few miles north to the south banks of the river Tyne some time after 1851. They are shown in the 1861 census as living in a village that was known as Felling Shore to the east of Gateshead town centre. Felling Shore was part of the civil parish of Heworth.
My tree shows that Alexander died in July 1865 in Gateshead, which was the Births, Marriages & Deaths Registraation district for Felling Shore village and Heworth civill parish. Gateshead was part of the old County Durham and is now a sizeable town in the relatively new county of Tyne and Wear.
In 1851, Irishmen Willliam Henry (age 34) and Robert Henry (age 24), who were probably brothers, lived in Felling Shore. Was your William born in circa 1817? This William might be much older than your ancestor.
The majority of my Henry ancestors came from from the civil parish of Kildress, to the west of Cookstown in County Tyrone, Ireland. Some came from other parishes in and around Cookstown (e.g. Derryloran) and one came from the nearby small town of Stewartstown. They were all Protestants and it would not surprise me if many were Orangemen.
It will be nice to hear from you if you think I've identified the correct Alexander.
Michael