At least in 2006 it was rather easy to get a tax identification number (I forget what it's called) with a signed affidavit and a witness saying you live at some address, and you can use that to get work. Now, without better documentation the government taxes you at the highest rate possible, and since you won't file you'll never get a penny back.
Also, they worked in card houses, so maybe the documentation requirements weren't as strict as a professional programming environment. Oh, and I'm sure it's all sorts of illegal. But just doing it is easier than it seems. :)
PPS Number
I suspect, but amn't sure, that this is more felxible, and I think they include Northern Ireland aswell, i.e. they include "the island of Ireland".
(Which makes sense, the country now known as Ireland didn't exit until 1922, I'm in my 27s and by grandmother was born in the late 1920s. Someone in the 50s could have a grandparent born in what was then the United Kingdom of Great Britain and Ireland.)