It's possible he wasn't registered with Kennedy surname.
This would make the search very difficult. I now believe that the Denis Kennedy I am looking for was born in England to an Irish family. We have very little information on him and my uncle's partner's family have just briefly mentioned a village called Dundrum and no relatives ever spoke about him.
I have found a Denis Kennedy living at Castleford near Pontefract on the 1911 Census. Denis's common-law wife (they never married) was from a Yorkshire Village called Kirkby Malzeard and their daughter was born in in Doncaster which is where they are listed on the 1939 census.
The Denis Kennedy living in Castleford was born in Prescot near St. Helens in the July-August-September quarter 1888. Although my uncle's partner's grandfather's date of birth was listed on the 1939 census as 26th July 1890, could it have been that he might not have known his exact birthdate? I have heard that some people weren't always sure of what year they were born.