Voltage, alternator, dash warning

[localshop]

It's an 07 yaris zinc mmt [Please don't - I inherited it ]

Driving along and all sorts of warning lights come on starting with 'battery charging' which soon disappears. I get almost home before almost everything stops. Power steering gone, won't change gear - the lot.
I get a tow home
I figure what connects all the faults is 'electrics'
The battery is a bit ancient so I pop another battery in and all is good - fires up and drives like a new one.

except
voltage as indicated by little plug voltmeter in the 12v socket is less than 12v when we're running [Little plug in voltmeter looks fine when plugged into another car]. Switch on headlights, ac and heated screen and it drops to 11.2v

There's no dashboard 'not charging' warning illuminated BUT - switching off and switching on again reveals the 'not charging' warning light doesn't seem to be working

I start by trying to change the bulb in the 'not charging' warming only to find the warning lights are all little LEDs on a circuit board.

I've replaced the Alt s fuse

Any clues where to go next other than 'get the alternator changed' which I've thought of already.

Many thanks in anticipation.