I'm normally not one to try and discourage people, but by saying things like "I was told to use the grey cable" it is clear you don't know what you're doing, and if you haven't notified your LABC in advance about the work you will be in violation of the building regulations doing it. I would strongly suggest you get a professional in to do this for you (it won't cost that much, and will ensure that it's all correctly installed and tested etc)...
However, in general, shaver sockets get wired in to the lighting circuit. You need to know what the fuse/breaker is on it to ensure it's sufficient, make sure that the lighting circuit is RCD'd (everything in a bathroom has to be RCD protected under 17th edition regs), and ensure the shaver socket is BS EN 61558-2-5 compliant. Generally for a lighting circuit 1.0mm or 1.5mm T&E would be the cable to use, but it depends on the breaker on the circuit, and the route taken by the cable etc.
If you do want to wire it to a ring main, then it would need to be wired via a fused connection unit, wired either as an extension to the ring, or as a spur. Again, make sure the ring main is RCD'd (or if not, you need to put an RCD protected spur in)...