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My battery light has been sometimes staying on after starting the car and coming on intermittently while driving. Battery was replaced earlier this year. Have tested battery post voltage using multimeter, 12.1V engine off and 12.9V engine on (while battery light is off).
Alternator wire/connection (assuming ground wire) seems damaged, see pics here:
https://tinyurl.com/caldalt1
https://tinyurl.com/caldalt2
Is there any way to check if the damaged wire is causing the issue?
It sounds like your charging system is starting to fail,
I would take the vehicle to an AA Service Centre, or Electrician to investigate the alternators performance.
The main positive cable does appear to be in poor condition both corroded and overheated, that could well be the issue.
If the charge light remains on eventual the vehicle may run out of power to continue driving.