If you're handy with a voltmeter...

First, check the battery voltage when the engine is switched off. It
should be around 12.5V if the battery is good and charged.

Next check the voltage at the battery terminals when the engine is
running, IIRC it should be around 14V if the alternator is working
properly. If it is much lower than this (~12V or less) then the
charging circuit isnt working, which would be causing your light to
come on.

If this is the case, check the voltage at the terminals on the
alternator (disconnect the wiring from the alternator, attatch
crocodile clips to the terminals while the engine is switched off, then
start it up. Keep your fingers.) This should also be around 14V and
shouldnt change if you rev the engine, If not then the alternator is
faulty.

If you have good voltage at the alternator but not at the battery then
the fault is somewhere in the wiring between the two, follow the wires
from the alternator/battery and check any connectors/terminals are
tight and corrosion-free.

Last time this happened to a mate it was just a nut had come off where
the circuit connected up behind the engine.

HTH
Andy

Hi mate ...check if the alternator is charging correctly (14.2 volts +/- 2
volts at the battery ) Also check @3,000 rpm .What should happen is once the
alternator output has matched the battery voltage the light goes out ,as the
exciter feed is obviously via the battery light.If not check the exciter feed
,do volt drop tests for the b+ lead and chassis earth ,If all checks out ok
the problem may well be with the instrument panel as in the past ive seen the
light resistor detach itself behind the clocks. let me know how you get on
all the best mark