Actually, Brompton does make their own case. But it's a soft case: Brompton B-Bag, soft Travel Case – NYCeWheels.com

Now we get into a counterintuitive situation with transport. You would think a hard case would protect the contents more. In reality, a hard case is more likely to get thrown around by airport workers than a soft case. So the hard case is abused more whereas more care is taken with a soft case. So it's not so much about protecting contents as it is what kind of treatment the luggage is subjected to.

You can find a suitable suitcase lots of places as tudorowen1 states above. I did exactly that a few years ago - took my Brommie M3L into a luggage shop and started trying each one on until I found one that worked. I believe I paid $30 and posted a thread here somewhere on it. Voyageur soft-sided case.