Re-reading your original message I see you did give the date of Arthur's death, from which it's been possible to find out what happened.

On 3rd January 1915 Private Arthur James Prior of the 13th Company, Middlesex Battalion, National Reserve was on sentry duty guarding a signal box beside the up line (London bound) at Forest Hill station.

At around 11:40pm he was struck by a train, possibly from behind, and died. A fellow soldier who was a witnesses at the inquest considered the sentry box to be in a very dangerous position, "the margin of safety being very little."

The jury gave a verdict of "Accidental death".

I'll upload a transcript of a newspaper report later.

So far I haven't found anything about his army service but may have found further personal details.

I think I've located his marriage in 1904 and the name of his wife, plus his home address when he died. I believe I've found him in the 1911 Census with his wife and three children, further to that I've found birth records of two children and another birth after he died.

Let me know if any of that information is of interest and I'll will forward it to you, I haven't given details incase those people are still alive.