You've tested it.  Inspection is just a small matter of removing the
gearbox, stripping said gearbox and looking at it.  ;-)

I'd try changing the gearbox oil for the LR recommended product.

Oh, I'm constantly dabbing it through the box without using the
clutch. Much easier than doing it properly! Makes a nasty noise when
you miss though. Changing down into 1st on the move is tricky under
any circumstances, it's a crawler gear with no pretence of even having
a synchro, and runs out at about 10kph. 4th is the bugger as the most
frequent change you have to make is 4-5-4-5-4-5 if the traffic isnt
maintaining a constant speed on the open roads. Probably why the
previous driver wore the gearbox out in the first place.

Alex

You have to double de-clutch to select a lower gear on the move on a box
without synchromesh. But this technique wasn't required when I took my
driving test some years earlier than you, and synchromesh first gears were
virtually unknown. Most cars with 'crash' first gears were happy starting
from rest in second - first only really needed for hills or with a heavy
load, so rarely if ever needed on the move. The advent of motorways meant
the overall gearing had to be raised - otherwise engines would blow up
with sustained high speed cruising, so first then became a gear which was
needed on the move. And synchromesh became the standard. Then 5 speed
boxes.

IIRC, the first mass produced UK made car with 4 speed box and synchromesh
on first was a direct relation of your Anglia - the MkI Cortina. The first
5 speed the Austin Maxi.

Some older cars had three speed all synchro boxes but these were often
four speeds with first 'blanked' off.

Your examiner may have been right to the letter of the regs on correct
use of the gears, but most would have made allowances for an older car.