Hi Sue
The original registers are at the Derbyshire Record Office in Matlock. They have been filmed by the LDS, so you could order the film up at your nearest FHC if that is more convenient.
Edgar's youth may be a clue. As a minor (under 21), he would have needed parental consent to marry. However, unless the marriage was by licence (unlikely), such consent was deemed given by default if his father did not object when the banns were called. If Edgar and Zillah were residing in different parishes prior to the first "marriage" then the banns should have been called in both. But many couples fibbed about this, mainly to save money. Edgar's parents could have found out about the marriage at the last minute and called it off, only to relent when they found out about the baby.
Do let us know what the answer is if and when you find out!
Caroline