They're not the best headsets, and I'm not sure Brompton do a good job of facing the head tube and fork crown at the factory, since this is the usual reason for a headset not being able to be adjusted properly. Unfortunately it's also a rather low stack height and therefore not many 1 1/8" threaded headsets will fit. I have a King 2Nut on mine but I had to cheat and grab 1.5mm more stack height by having the head tube aggressively faced.
The other fault these suffer from, at high mileage, is stretching of the head tube. I had an L3 that was about 9 years old, and the lower cup was very loose. Beware of any bike with pressed-in cups that isn't lugged or doesn't have reinforcing rings brazed around the top and bottom of the head tube! I fixed it with a suitable strong grade of Loctite.
Add it to the list of Brompton design faults they still haven't fixed after 30 years...
You should be able to adjust it without removing the stem, if the stem has been fitted properly according to Brompton's instructions. There should be a little daylight between the bottom of the stem and the locknut. If someone has pushed the stem right down when fitting it, you will not be able to undo the locknut without first pulling the stem up a bit. The stem wedge can take quite a hammer blow to make it drop.