I have a bank of switches for my shower room. One of which switches spotlights above mirror. My switch is earthed but when I look at the connected wiring 2 core comes from switch but I will need to connect 3 core to new led light with shaver socket. Am I OK just to connect 2 core to 3 core ?

I don't know what you mean by "2 core or 3 core". I suspect you are speaking EU or UK "Sparky speak". We only speak US "Sparky speak"

I think that you mean you have 2-wire (with ground) and 3-wire (with ground) cables.
If that is correct and both wires of the 2-wire cable between the switch and the light fixture are connected to the switch, then you will have another 2-wire cable in the light fixture box that brings power to the light fixture. If so, the neutral of that power in cable will be connected to the neutral of the fixture. The "hot" of the power in cable will be connected to one of the wires in the 2-wire cable going to the switch. The other wire in the 2-wire cable to the switch will be connected to the "hot" of the light fixture.

If all this is true, then you would connect the neutral of the power in cable, to the neutral of the new light (just as it is now) and to the neutral of the shaver outlet (if there is one. The two may be combined). You would connect the "hot" of the power in cable, to one of the wires in the 2-wire cable to the switch (just as it is now) and also to the hot of the shaver outlet. You would connect the other wire in the 2-wire cable to the switch, to the "hot" of the light fixture (just as it is now)
I do not know your wire color scheme for hot and neutral but you should. I do know that you have two schemes. Be careful.