This is a real puzzle. Like Cathy, I have tried to connect Woodbridge/Roadnight/McDonald but it isn't happening. There are so few McDonalds in Bucks. !!!
Another thought, probably a long shot & way off target but could Arthur have been a "Home Child". I have been googling & found info on "British Home Children" that were sent from England, Ireland & Scotland from 1869 to 1939. They were children from poor homes, workhouses & orphanages. Have only just skimmed the pages so I'm going back for another look.
I'll let you know if I come open anything that could be relevant & as Cathy said, keep us posted on what you find.
Cathy & Maddie, thanks I have not heard of this site but will certainly try yes it is possible that he could have been a home child and that I have been on the wrong track. My information about him comes via an elderly aunt (his daughter) and although I have questioned her several times and the story remains constant she does at times tend to wander. I tried the adoption people here in Aust. without luck but this means little as he may well have been an agreed adoption at any rate records did not start until the late 1920s If only I could find his arrival here then the search would become easier but there are a number of ships that I am unable to find passenger lists for. I just keep on searching .... regards beau