Before we rush to Fenton, I have heard back from the school where Frederick and Cedric went. They have confirmed that their father WHB died between 1908 and May 1909 which fits with the WHB born in 1857 to William and Sarah. I have invited the lady that has been looking for him on GenesReunited to this thread to compare notes (and to probably make this the longest thread in rootschat history!)
The school also told me that Frederick achieved some notable successes, including the highest score in the entrance exam for Sandhurst in 1913 and was mentioned in dispatches in 1919. Sadly, he died in 1927 aged 32 while in hospital undergoing an operation. It looks as if from the five children of WHB mine is the only surviving line