An update.
After buying a new multimeter, the current through the white wire at the regulator is 2,5A with a voltage of 12,6. Bearing in mind the resistance of the coil, 2,9-3,0A would be “right”. It didn’t make sense that the current was 0,04 and the battery was still getting some charge.
I refitted a voltage monitor (single LED that changes colour with voltage) and had a short ride yesterday. This said the battery is being overcharged at anything over 2500 rpm. I checked this with my new voltmeter and this is indeed the case. If I keep revs to between 2500 and 3000 with the headlight on, the voltage remains in the 14V area, which should be OK.
So as several of you suggested, it looks like the regulator is the problem. I have bought one on eBay that I should get sometime this weekend, so fingers crossed.
The only thing now is, when I ride, If that little light flashes red, (>15,2V) I get all worried that I’ going to fry my battery; beforehand, no light, no worry!