If you look for Robert Franklin born in Lincolnshire from 1920 to 1939, you only get one hit. So either Bingo, or wrong years, or born elsewhere. (Glanford B, 1923, too old?)
There is a possible marriage of a Robert Franklin in Glanford B in 1922 to a suitable mother (Ada), but then no birth for an Arthur.
Robert, Robert and Ada are together in Scunthorpe in 1939.