I've tried the Alfine hub on the Cadenza 08 and it really is a beautiful shift. For me this is a realistic alternative to adding a Rohloff hub which would be OTT for the Brompton.
Now I know that people have successfully fitted Rohloff, Sturmey Archer and Shimano Nexus 8 speed hubs to the Brompton. The Alfine is listed below:
The only challenge seems to be the OLD measurement is 135mm compared to less on the others such as 131mm for the Rohloff and 124mm for the SA X-RF8 . Would this problem be surmountable?