i was going to say if you needed a 105amp alternator i have a spare one which i could of let go for a small amount lol just collecting dust here.
even that checks by some garages cannot point out some faults that give the battery charge light. mine for example, i had the battery light constant. i went and checked the voltage on the battery was a bit low so i got the battery changed just incase a cell had died, light stayed on. went to a few garages/auto electricians they checked, scratched their heads and said could be the alternator so bought a new alternator and fitted it - light still on so the alternator was ok. checked the wiring as best as i could. turned out the ECU reference wire in the wheel arch was snapped. apparently this is really common on the focus's and transits.
you will find however, the heated windscreen wont work when this battery light is on. as this take's so much juice. it is also that taxing on the alternator/battery it is timed to auto turn off 10-15 mins. the back window heaters are timed but dont take as much power and so will stay activated.
with the engine running and a few revs given, everything on, the alternator should kick around 14.5v out. engine off, battery should read anywhere between 12.5v to 12v.
if your engine is running and everything is on, and your alternator is showing as kicking out 11.5v or lower, the alternator has gone into conventional mode and should show the light on the dash. as you say its kicking 10.5v...i would use a multimeter and get someone to put it to 2k revs and see if it increases correctly. if not i would suspect these wires and carry out checks to save you some £££'s of buying a new battery and or alternator first.
thanks for that post...I have done the load test and rev'd the engine, although I couldnt read the multimeter myself my friend said that the voltage hardly increased. I dont beleive it's a wiring issue, because there is a whining sound that changes with the speed of the engine