LEDs on 240v

I do not like any circuit connected directly to 240v mains. However Christmas tress lights (globes) have been connected directly to the mains for 30 years without any major problems. 

Insulation must be provided and the lights (LEDs) must be away from prying fingers. 
You need at least 50 LEDs in each string to prevent them being damaged via a surge through the 1k resistor - if the circuit is turned on at the peak of the waveform. As you add more LEDs to each string, the current

will drop a very small amount until eventually, when you have 90 LEDs in each string, the current will be zero. 

For 50 LEDs in each string, the total characteristic voltage will be 180v so that the peak voltage will be 330v - 180v = 150v. Each LED will see less than 7mA peak during the half-cycle they are illuminated (because the voltage across the 0.22u is 150v and this voltage determines the current-flow). The 1k resistor will drop 7v - since the RMS current is 7mA  (7mA x 1,000 ohms = 7v). No rectifier diodes are needed. The LEDs are the "rectifiers."  Very clever. 

You must have LEDs in both directions to charge and discharge the capacitor. The resistor is provided to take a heavy surge current through one of the strings of LEDs if the circuit is switched on when the mains is at a peak. This can be as high as 330mA if only 1 LED is used, so the value of this resistor must be adjusted if a small number of LEDs are used. The LEDs above detect peak current. The LEDs are turned on and off 50 times per second and this may create "flickering" or "strobing."  To prevent this flicker, see the DC circuit below:

A 100n cap will deliver 7mA RMS or 10mA peak in full wave or 3.5mA RMS (10mA peak for half a cycle) in half-wave.  (when only 1 LED is in each string).

The current-capability of a capacitor needs more explanation.  In the  diagram on the left we see a capacitor feeding a full-wave power supply. This is exactly the same as the LEDs on 240v circuit above. Imagine the LOAD resistor is removed. Two of the diodes will face down and two will face up. This is exactly the same as the LEDs facing up and facing down in the circuit above. The only difference is the mid-point is joined. Since the voltage on the mid-point of one string is the same as the voltage at the mid-point of the other string, the link can be removed and the circuit will operate the same.

This means each 100n of capacitance will deliver 7mA RMS (10mA peak on each half-cycle).

In the half-wave supply, the capacitor delivers 3.5mA RMS (10mA peak on each half-cycle, but one half-cycle is lost in the diode)  for each 100n to the load, and during the other half-cycle the 10mA peak is lost in the diode that discharges the capacitor. 

You can use any LEDs and try to keep the total voltage-drop in each string equal. Each string is actually working on DC. It's not constant DC but varying DC. In fact is it zero current for 1/2 cycle then nothing until the voltage rises above the total characteristic voltage of all the LEDs, then a gradual increase in current over the remainder of the cycle, then a gradual decrease to zero over the falling portion of the cycle, then nothing for 1/2 cycle. Because the LEDs turn on and off, you may observe some flickering and that's why the two strings should be placed together.