Assume you have them in 1871 at 13 Plato Street in Leeds. Alice McElroy is shown as Widow, all shown born Douglas.. They are on the LDS IGI in 1861 in Douglas as McLaisy (Lawsons index as McClroy) with 5 children including Elizabeth that Frances found for you,
Alice is shown born Douglas as are the 5 children.
The 1851 Lawsons Index for the census they are listed as Muckelry.
I cannot find any of the family in 1881, looked for second marriage of Alice , could not find.
On the UK Free BMD , you can search for a death of Henry with any surname , but due to quantity you have to restrict to County or District. Checked Leeds , then West Riding of Yorkshire and found no name beginning with M that looks like him.
There is also the possibility he left the family and went back to Ireland.
I have been trying to find my Great Grandfather in Ireland born around 1844/5 with my Scottish Cousins for about 20 years ...............found nothing, Ireland very frustrating.

David Dwyer