Finding information about Matthew O’Neill and family

Hi there, 

I have been researching the O’Neill side of my family, who come from Tyrone. I believe from Ardboe.

I found a wealth of information on Ancestry but after looking more closely I fear people have added people to trees without checking they are definitely who they are. As such I have simplified my tree down to start again with information I am a lot more sure of.

The information I have as of yet is as follows: 

My great grandfather was called Matthew John O’Neill - he was born in Ardboe, Tyrone on the 18th of February I believe. His wife’s name was Alice. They had 11 children (I believe. My grandparent being one)

They moved to London in the 1960s, and he died in Newham on the 25th of March 2004. Alice died in Newham too, on the 25th of April 2015.

I am aware that it’s hard to find more recent records, so I’m more interested in finding Matthew’s parents and Alice’s too - especially as I am unsure of her maiden name. 

Matthew’s parents are listed for his baptism as Henry O’Neill and Sarah Mcevoy, with witness Christina O’Neill. I am unsure from my research if Henry’s name was Henry or if he was Joseph Henry O’Neill, as the dates of a man of that name match up.

I would love to find out if I am going in the right direction with this as would absolutely love to find photos or just information of my ancestors.

Any help or advice would be endlessly appreciated!