should have wire 110v  circuit with  an earth leakage protection device, tripping current 30mA  or less, otherwise power service provider will not be allowed

should have wire 110v  circuit

Not this side of the pond! 230V is normal in bathrooms in the UK, although you're right about 30mA RCD for additional protection for all circuits.

Is it possible/allowable to spur the LED Mirror and shaver socket from the power socket?

Usually yes, I'd expect the shaver socket to be OK directly on the socket circuit, but the light will probably need fusing down (typically a 3A fuse in a fuse connection unit) - do but check manufacturer's instructions for both, as some may differ. One spur feeding both isn't a conventional circuit arrangement, but provided the loads are small (as they seem to be in this case) it should be physically fine. The new FCU wants to be outside zones - preferably in the other room (alongside the socket?). Unless the shaver socket is more than 2.5m away from the shower tray (or 3.7m from the shower head if it's a wet room) it'll need to be of the isolating transformer type. Check too that the light manufacturers state it's suitable for bathroom use (and for whichever zone it ends up in).

If the new work is within zones (e.g. <600mm horizontally from the shower tray) it will be notifiable work under building regs (part P) (in England/Wales at least) - which can be surprisingly expensive. In any event, to comply with BS 7671 you'd need to be able to test and certify your work too.

   - Andy.

AJJewsbury said:

Not this side of the pond! 230V is normal in bathrooms in the UK, although you're right about 30mA RCD for additional protection for all circuits.

I believe bathroom/shower room, at least some circuits under NEC (USA) require 10 mA GFCI protection - certainly socket-outlets, although use of an isolating transformer is not needed where 10 mA GFCI is used?

And while a socket circuit should have RCD protection already, in a new ish build, certainly the bathroom bit of any new wiring needs it. Realise also that not all shaver sockets are created equal and the kind needed in a bathroom needs an isolation transformer to meet the UK regs. Those designed for bedrooms, or continental bathroom use don't normally have this, and the mains arrives direct at the shaver outlet.

so 1st question Kevan, where in the world are you ? - voltages and regs differ widely.

Mike

AJJewsbury said:

Usually yes, I'd expect the shaver socket to be OK directly on the socket circuit, but the light will probably need fusing down (typically a 3A fuse in a fuse connection unit)

Agreed. The shaver socket should specify the upstream protective device. Both could be supplied by the same FCU.

mapj1 said:

Realise also that not all shaver sockets are created equal and the kind needed in a bathroom needs an isolation transformer to meet the UK regs.

Isn't the point of UK shaver sockets that they have an isolating transformer built in, which was what we had long before RCDs?

Chris Pearson said:

Isn't the point of UK shaver sockets that they have an isolating transformer built in, which was what we had long before RCDs?

The "bathroom" type of sockets, yes indeed. There also exists a "bedroom" type though - without an isolating transformer (usually single gang size and with only  230V output) - e.g.the old MK K700 WHI

   - Andy.

Also  there are mirror cabinets which look like and are sold as bathroom cabinets made for use in countries without this requirement, that  do not include this isolation. I've got  a rather nice 'Allibert' model like this at home - it allows continental relatives to use their favourite hair tongs or whatever on a 2 pin plug without things going 'phut' at a key moment. But it would never pass a BS7671 EICR, and as such is installed to the VDE standard of the day instead (don't ask!).

The problem may arise when folk order from abroad off the internet and do not always appreciate that in the UK they adopt the legal responsibilities/liabilities  of an importer when they do so, to make sure it meets UK requirements, and a reputable sparks whose scheme only permits him/her to work to BS7671 may be unable to install it despite the CE mark.

Mike.

Oddly enough, if you were actually based in Sri Lanka, the mains there is 220-240V and the old round 3 pin UK style sockets and 13A square pin sockets are common.  The only high population places still using 110V are Japan, Canada and the US, the latter tends to dominate the available literature, making it appear that 110V is more common than it really is. Northern Brazil is a bit mixed as are parts of the middle east . This map helps illustrate.


Mike

The US actually uses 120V (and either 240V or 208V).  Increasing it from 110V to 115V and then to 120V allowed them to push a few more watts down the wires for the same current.

You are right of course, and strictly Japan is more like 100V, but I was more concerned about the voltage doubling than the 10% tolerances. I'm always surprised how little the USA use 3 phase, in anything but a large factory unit it seems the best you can get is what we would consider to be split phase. That and some weird 'odd-leg' arrangements and transformers in places where on 400V you would not need to bother. 
Electricians United by a common set of physical laws but separated by widely different implementation.

Mike.