The bridge rectifier outputs rectified DC with no filtering.
As the peak voltage exceeds the battery voltage by approximately 2 volts SCR BTY79 fires due to current thru the 470 ohm resistor and the 1N4001 diode. This occurs two times per AC cycle and the battery is connected to the rectified DC. The battery now charges.
The battery voltage is applied to the 1.2k ohm resistor and the 4.7k ohm variable resistor. When the voltage at the variable resistor wiper is high enough, current flows thru the 6.8 volt zener and fires SCR C106D.
This action pulls the 470 ohm / 1N4001 diode junction low thereby removing gate drive to SCR BTY79. The battery stops charging. The CHARGED LED turns ON due to current thru the 470 ohm resistor and SCR C106D.
High leakage inductance likely limits charging current
the basic SCR battery charger you show has appeared in several variations over the years. Here's a link to the same schematic you posted. I consider it to be crude but apparently it's effective enough. I believe the transformer has high leakage inductance to limit the battery charging current.
As long as one understands how SCRs operate figuring out how the circuit works is a simple matter.
