OK, I have cleaned my ground strap at the battery negative, and checked again. Turned on all consumers, headlights, fog lights, rear windshield heater, blower motor, etc, and it charges only 11.9v idle.
At about 1200 or above it charges fine.

My ground strap however looks ancient, and it's torn halfway by aging, so its definitely need to be replaced. I also need to check the ground strap at the bottom, between transmission and vehicle body, as I remember from last week, it was quite full of oil and dirt, so it might worth a check.

Are there any other ground straps on this car I need to look after, before visiting az automotive electrician with my possibly faulty alternator?