This hardly covers all generations of course and hardly disproves that there is a Belgian connection. This is translated from Celtic to "English" and back again in both of my sources. So the name "Mac Vaddock" is in Celtic Mac Uadog and also back to Engish in these two books Mac Vaddock.
The question of which came first, the Celtic or English (or even Belgian) is not really convered in what I read.
If you read my previous posts from the "Book of Rights" you will see that this is not just a matter of Landowners rights but that this family is descended from the so called "Kings of Leinster" in Ireland. Not the greatest classification in the world but the source does say that.
Also you can check out the post of Dick Weadock at this Weadock page on the subject of our supposed Beligan connection.