I am glad that you have your father's birth record, which gives you a connection to his parents on a paper record. The next thing to go for, normally, is a marriage record for your father's parents, because the marriage record contains the father's name and occupation for both the bride and groom, and so this would give you a connection between your grandfather and your great-grandfather on paper. Unfortunately, your grandparents did not marry, so you do not have that paper record. What I normally do in this case is visit the cemetery to locate their gravestones and get their birth and death dates, and then I visit a local library or archives to look for their obituaries in old newspapers that are saved on microfilm. Alot of times, obituaries contain the names of relatives, which helps to assemble families.
I believe that John Devlin was born circa 1858 in Ireland and died in either 1899 or 1900 in Middlesbrough. I believe that Martha Sweeting Devlin Hold Lewthwaite Carter was born in 1870 in Durham County and died in 1933 in Middlesbrough. There is a record for a William Devlin who died in the April-May-June quarter of 1942, age 56, in Middlesbrough. That age is two years off, but close enough to possibily be your grandfather. It would be interesting to learn if these folks are buried together, and see if obituaries exist. Have you visited the cemetery in Middlesbrough?