Ah,.. Sorry, I forgot to check that side of the schematic didn’t I?
The centre-tap of the transformer connects to the 0 volt line and I would suggest that the charger (low volts) circuit is ISOLATED from the case entirely. This ensures that accidentally dropping the live lead on the box does not burn something out or frighten the life out of you with the spark.
Certainly connect an earth point to the case to prevent any mains failure from making the case live.
So, the circuit should now look like this,… with your 18-0-18 transformer you should then have a positive line of 25 volts DC, in which case C1 should have a working voltage higher than that and I tend to allow for transients 10 volts above so it would be 470uF, 35 volt working at least.