Just for a broader perspective on strategies, I've used no padding whatsoever, just have been dropping our Brompton into the B&W case and taking off, no straps no nothing. Over time I ripped a bit the foam that the B&W case comes with and filled the damage with spray-on construction foam - works very well. Even that ripping has been mostly done when I forced our Dahon bikes into the case - they don't fit as well a Brompton.
The Brompton does fill the B&W case fairly well, so you're probably fine with it as is. When I got the B&W case though, I skeptical about the rather thin padding it came with, so for a cheap investment of $30 of foam, I figured that cost was worth it to protect an $1800 bike. Now that the bike has been through a bit.. meh... it'll survive. I figure better safe than sorry, so I continue to pack it the way I do. It only takes about 10 minutes to pack up the way I do.