Are you talking about an 8-speed Alfine hub? That one has a OLD of 135mm, whereas your nominal Brompton OLD is 112mm. So custom spreading of rear triangle, or buy a kit that already has a new rear triangle like the Kinetics below, tho won't be cheap.
Brompton Alfine Kits ? Kinetics
Probably the most cost effective way is to get a multispeed hub that nearly matches your Brommie OLD (no rear triangle spreading required), like a five-speed S/A S-RF5 with 111mm OLD, hub only at $125:
Sturmey Archer S-RF5|-Brommieplus-Products
...and have a wheel built around it and then installed (or buy one from brommieplus already built up but more $).
Yes, I agree you've got to find someone who knows what they're doing, as there might need to be modification to the cable routing to accommodate the Brommie fold. It wouldn't necessarily have to be a folding bike mechanic, just a mechanic who knows enough to allow for routing the cables to accommodate the fold.