I think you should also answer a question:
Why to use safety rated capacitor in a capacitive dropper?
AFAIK the idea of your supply is that it does not offer any protection, thus no safety rating needed. Well, had you used insulated capacitive dropper, then maybe this could have its place but otherwise - I do not see the point.
Yes, interesting question. The capacitor doesn't actually
need to be X rated as it's not a direct across the line application. A 630V rated capacitor would serve in this application. However it is important to ensure that the implementation is safe (as safe as a non-isolated PSU can be) particularly fire etc. An X rated capacitor carries agency approvals, which provides some level of assurance of flammability etc. even though it might have thinner metalisation and therefore more prone to capacitance loss through self-healing. I mentioned also, the use of a fusible resistor. Again, it's important that the implementation is as safe as possible.
With regard to the 'Insulated' PSU that you linked. That's a difficult one. Yes, having a series capacitor in both legs does make it L/N orientation insensitive, but it also guarantees that the circuit is floating at half-mains potential in all cases (with significant current capability) - It also means that the capacitors will be twice the value, further increasing the current capability in a contact to ground situation. Obviously, no part of the circuit or its inputs / outputs can be user accessible, they need to be treated as being at mains potential.
I think 'Insulated' is the wrong term for this circuit. it only provides any insulation with DC on the input (and of course no output in that situation). It is most certainly
not insulated when driven by AC mains. [EDIT: The article also says "totally isolated from mains supply", which it is certainly NOT - this is a dangerous statement!]
As mentioned, it does make the circuit L/N insensitive which may help in some countries with non-polarised mains connectors, but as the OP is in the UK, with defined polarity on outlets, I think that the disadvantages outweigh the single advantage.