I've got 12.6V 3A transformer that I'm now using. I set the pot to half way turn on the charger and connect the battery. The LED is on and when I turn the pot the LED turns off and the voltage rises to around 13.6V and the LED flickers. I'll keep it connected for 20 to 30 minutes and the voltage drops down to 13.5V.
R1 and R3 are 330 ohm and R2 is a 100 ohm pot. D3 is a 1N4734A 5.6V 1 watt zener diode and it's connected the same way as in the schematic.
It sounds as though the charger is operating as it should. The voltage rises to the cut point when the LED begins to flicker. Left alone it will eventually turn solid. The difference of 0.1V is negligible.
If you can't get a voltage higher than 13.6V, then try another 12V transformer.
I've got another circuit that the SCR is a BT169D and the voltage on this one will go past 15v and the LED never comes on. The other circuit uses a X0402MF 0AA2 for the scr and this one never goes above 13.6V.