We now know that the Nazi Occupation Authority in place had orders to make sure that all children under 13 had to be "registered", and that this was before the Very Bad Thing occurred.
I'd like to point out that, according to death screen, Arthur was born in 1934, i.e. he was 13 in 1947 when the order was issued. Would he be considered young enough to be registered, I wonder?
Also, unless Percy is just freakishly tall, he's older than Arthur, therefore he probably wasn't taken away with other children (the audio flashback from E3 trailer seems to confirm that).
And now, here's my theory about what happened to the children:
Personally, I think Nazis were developing some sort of brainwashing technology for turning civilians on occupied territories into perfectly obedient war machines, so they rounded up the children in order to use them as lab rats (because a child's brain hasn't finished developing yet and therefore more susceptible to outside influence, or something). Having their children taken away was the last straw for the citizens of Wellington Wells, and they started a rebellion. The Nazis decided that that was a perfect opportunity to test the fresh batch of little soldiers of Wehrmacht in the field. And that's what The Very Bad Thing means - in order to drive out the invaders people had to kill their own children. Afterwards the Wellingtonians were naturally wracked by guilt, so, in order to forget what they've done, they had to resort to drugs, ironically, the same ones that were used in brainwashing their children.
I know, this theory doesn't dwell into the debate if the Nazis really were gone after WW2 supposedly ended, or who's running the show in the UK, or if the rest of the country is also a combination of ruins and Orwellian drug paradises, or how our intrepid protagonists tie into all that etc., but frankly I don't have any coherent ideas on those points.