Can a Shaver Light cum socket be connected to the Earth instead of the Neutral ?

Spot On. There is a junction box behind the Extractor Fan Switch and the Neutral there was not connected.
Connecting that completed the circuit and I can see 245 V across the Live and Neutral of the Shaver Point now.
However, the Extractor Fan is not working, which could be due to the fact that I left the yellow (with the Red Sleeve) disconnected in the Pull Cord Switch (as shown in yesterday's photos). I guess that is the wire that signals the Extractor Fan to switch On/Off when the Main Light is On/Off. I'll connect it and check.
I'm uploading the photo (Black Wire with a bit of White Paint was not connected).

It could be, but you seem to be one cable short in your pull cord (permanent live feed)

It would lead me to believe you have a junction box somewhere that joins the permanent live from the circuit to the fan feed and the pull cord, but this is somewhat illogical.

I would test to confirm that the red from the 3C+E is indeed permanent live, and both that the yellow has continuity from there to the fan and that the other red in the switch is the switched live.

One of them is permanent Live (Tester glows).

Well yes that's a given. But you need to prove the other two points, with a multimeter.