Sorry, hate being a prophet of doom.
Even though all births, deaths and marriages were supposed to be registered, even in 'normal' circumstances people didn't for a vast amount of reasons.
Maybe if you concentrate on Mary White and her parents / siblings with time something may come to light.
If you use a site like ancestry to enter your tree on, and add on EVERYTHING that you have, you never know what information you may stumble across.
With time, also myabe a family member may be more forthcoming with new information.
By the way, did William put an occupation down for his 'father' ?
Tara