Firstly,
a big thank you to everyone who has taken the time to read and to reply.
Cornelius Harrington (DOB ranging from 1854 to 1866. He was actually born in 1854. There is no birth certificate but there is a catholic baptism record. He was baptised at St Mary's, Horseferry Road, Westminster.
He married Mary Williams (my gt grandmother) in 1884 at St Mary's, Horseferry Road.
On the 1884 marriage certificate it states that he was a widower, a builder's labourer and his father was Cornelius Harrington - labourer.
I've never been able to find him on the 1881 census. On at least one census he is listed as John - whether this was an alternative name or whether he had actually said "Con" and it was misheard is unknown. And his age varies between census and he was actually 8 years too YOUNG on his death certificate. I do know I have the correct Cornelius Harrington though as the other members of the family are people I can identify.
So to his first wife........A Cornelius Harrington married a Mary Sullivan in a catholic ceremony in 1875 at St Mary's Horseferry Road.
Cornelius gave the correct age. He was a labourer and his father was Cornelius Harrington, also a labourer. And though it isn't definite proof in 1875 Mary Sullivan lived at No. 4 Johnson's Court, Westminster, whilst in 1884 Mary Williams lived at No. 5 Johnson's Court, Westminster. It's an interesting coincidence if nothing else.
As for children from the first marriage?
I've checked the gov uk certificates online birth index for children of either gender from the years 1875 to 1884 with father called Harrington and Mother's surname Williams. There are a total of 5, 4 were born and registered in Wales but there is a more likely birth in St saviour Southwark in 1877. An Ann Harrington. If she was their child than Mary Sullivan was alive up to 1877. I'll only know for sure if I get the birth certificate. There is no sign of Ann on any later census' living with Cornelius and his second family.