I don't know where it comes from, I just know that it so irritates me when people say it, cos the saying is "19 to the dozen" meaning working faster. surely if it were 10 then they'd be going slower. i have a friend who always uses this phrase and when he does i always say 'so they were going slow then' - he doesn't get it! lol
If I may ask, are you from the South or North of England? I grew up in the North and it was always ten to the dozen, which as always confused me.
Just read on one of the links that it means, more or less, that the speaker is talking so fast that the listener only hears ten words to the dozen. Makes sense now.
I'm from neither North nor South, but right in the middle, and it's always been nineteen to the dozen round here - ie, cramming in far more than you've really got space/time for.