Hello Donna, I have searched for your William Barry in the 1939 English register and none are listed with the DOB you quoted, was William his known by name or given name, and what is the name of your grand mother, and / or children of the family? Do you have a tree at Ancestry to share?
I am an ex admin for the Barry surname project at FTDNA , and they run a autosomal DNA project along side the Y DNA as per Ancestry or 23andme or FTDNA testing, which has to be loaded into Gedmatch to compare to other Barry families.
From my own experience you need to also search for the surname Berry, there are only a few William Barry in the 1911 Irish census born in and around Co Cork, and the web site for Irish BMD is down at the time of writing which would hopefully would have given more details about his family in Ireland.
If he made a will then there might be a probate record for William, so what I'm saying is that we need more specific details of the two families , and when he left Ireland.
My great grand father Michael was married before he came to England, but didn't as far as I have found have any children in Ireland, but shortly after arriving in Portsmouth he married a local woman and had a large family, so I'm not supprised that there was a second family as legal divorce and seperation were not common for working people.
I'd be glad to help with looking for your relatives or missing children you can contact me directly at mike@family-barry.com