I'm curious, how do you know the generator is "putting out"? The light on the dash essentially compares the generator output voltage to the battery voltage; so it will not be on if the generator is putting out 12v.
In your case, I would start by double-checking the wiring; especially to the 'ignition' lamp on the dash. It does not get grounded, but should have one side connected to the ignition circuit (white wire), and the other side connected to the charging circuit (yellow wire to 'D' terminal on control box). Also double-check that terminal 'D' of the regulator is wired to the big terminal on the generator, and 'F' is wires to the small terminal.
Then try repolarizing the generator. One way is to remove the wire from the 'F' terminal and briefly connect it to 'A' or 'A1' (engine not running). You should get a little bit of a spark.
If that looks OK, use a voltmeter to check the voltage from 'D' to ground with the engine running. If it is nearly zero (less than 1 volt), then either there is a short to ground or the generator is defective. In that case, remove the wire from the large generator terminal and check directly on the terminal (which may require removing an air filter and/or some of the linkage). If it's still less than 1 volt, the generator is bad (perhaps an internal short, or a brush not making contact).
If the voltage at 'D' is around 2-3 volts, the generator is probably not getting field current for some reason. In that case, check the voltage on 'F' which should be the same as 'D'. If not, the control box is defective or very badly misadjusted. If both are around 2-3 volts, then check at the small terminal on the generator. If it is the same, the generator is bad.
Go
here and download the "Lucas Generator and Control Box Tests" booklet. It gives a detailed test sequence.