I recently bought a couple of SES LED lamps (**broken link removed**). When I used them I noticed some 100 Hz flicker, so I had a look. The clear cover unscrews so it was quite easy to get to the circuit.
There's a 560 nF current limiting capacitor giving about 40 mA rms on 230 V, 50 Hz. That goes through a full bridge rectifier and charges a 4.7 μF, 250 V capacitor. The 15 white LEDs are all in series, along with a 200 Ω resistor, and that lot is connected across the 4.7 μF capacitor. The LED voltage is around 50 V, including 8 V or so across the resistor.
The 4.7 μF capacitor is far too small. The average LED current is about 40 mA, and at that current, the capacitor voltage is falling at about 8600 V/s, so there is no way that could go on for 1/100 seconds. Looking on the oscilloscope, the LED current dropped to just about zero each half cycle.
I don't know why the capacitor was so small. It was rated at 250 V, which is very generous, but you would still get problems if the LEDs went open circuit. If they did go open circuit, the voltage would rise to about 325 V so it would still be overloading the capacitor. The lamp would have failed by then, so what happens to one component in the lamp doesn't affect anyone much.
I've changed the capacitor to 47 μF, 100 V and there is now now visible flicker. Each half-cycle, the current varies by about 20%.