What's the build date (stamped on the hub)?
Don't see one, but it's a Sun-Race Sturmey-Archer so I know it's post-2000.
I found that the other day Googling. Section 2.3 seems to have some bearing:
2.3 Hub Bearing Adjustment
The right hand cone is preset at the Sturmey-Archer factory and should only be disturbed during a major service. The left-hand cone only is used for normal bearing adjustment.
1. Loosen left-hand cone locknut.
2. Adjust brake arm nut until very slight side play can be felt at the wheel rim, and none at the hub.
3. Holding the brake arm nut stationary tighten the cone locknut (Torque 27 Nm).
I tried loosening the cone locknut, but I couldn't budge it. That and the brake arm nut are an odd size, too. I'll have to come up with plan B.