I assume this is probably a regulator fault but thought I would post on here anyway in case there is a TF quirk. My battery ran low a few weeks ago due to near zero car use. Charged it. All well. And from this I know the alternator was putting out about 13.8, because I measured it at the time. Today, a few hours after retrieving the car from the MOT tester, I noticed the alternator light was on. Checked the voltage - 13.2. Engine off. Engine back on. Light out. But voltage still 13.2.
Before you do anything, check that the connections to the battery, alternator starter motor and ground are clean and tight.
Shitty conections can impair optimal charging performance.
"Keep calm, relax, focus on the problem & PULL THE BLOODY TRIGGER"
The battery will drag the voltage of the alternator down a little bit as it charges the battery up. I noticed this as I charged mine up after jump starting it when flat and then running the car and monitoring the voltage from my built in voltmeter. It gradually climbs as the battery charge increases. Mine took about 30 mins to creep up from 13volts to 13.9 volts while driving, It could be that your battery has seen better days. Also remember that running the heater fan will drop the battery charge a little, as will lights, rear windown heater if you have one etc. Switch all these off to get a true reading of your battery.
The battery is less than 2 years old. The readings I obtain are quite erratic, and don't correlate with the alarm light being on or off. I will need to monitor this for a while....