Alternator voltage regulator: symptoms

1995 Micra.
Started up OK this morning, drove OK for a couple of miles. Then, the
engine suddenly cut out at a *busy* junction.
The car would not restart, ore even turn over. Symptoms were of a flat
battery. Dashboard lights were out.
The car has recently developed a tendency to stall at junctions, but
has always restarted immediately.
Anyway, I called Green Flag out.
The mechanic put a booster on the battery and the car restarted
*immediately*. He measured the battery voltage: over 14 Volts.
He then did some measurements on the alternator output and told me the
alternator voltage regulator was knackered. And that I needed a new

I then drove the car home and stopped the engine. I then immediately
tried to restart the engine. Same symptoms of a flat battery. Engine
would not turn over. I read the battery voltage, it was 12.4 V.

So, is it the battery, or the alternator that is faulty? If the
battery was healthy, wouldn't it still have enough charge to start up
the engine, even if the alternator was kaput?
Or is the problem that the alternator is not recharging the battery at
all? If so, why did the car start first time this morning?