I'm not aware of this topic being discussed on this forum before. I have a brompton with a rear rack. I've been looking for a decent luggage solution for the bike. Now, I know that brompton front carrier block along with their bags are an elegant solution. But, they are a bit expensive and were not large enough for my use. Besides, I like options and I am sure everyone does. I've been using the xootr crossrack along with cross bag for some time. But it just wasn't working for me. Head over to my thread about that if you are interested.
The Brompton has a sturdy rear rack, and I wanted to use that to carry my stuff. Then I started following these guys from "Path Less Pedaled". Here is Russ explaining his method for mounting a backpackers backpack on the back of a brompton. I stole this idea from them, modified it slightly for my use and it works great. I'm carrying a SwissGear 1775 Black Backpack. Let me know what you guys think.
Head over to Path Less Pedaled to learn about their awesome trip.

That's great, thanks for sharing! What is the bar under the saddle that you hang the backpack on?

The bar is an old handlebar. I cut it down to size, wrapped it with an old inner tube and added some bright red endcaps.