[Kalkanites]

Hello

I have acquired an old brass desk lamp which has two core wire using a brass bulb holder without an earthing connection.On stripping the light the two wires running throughout the lamp were unsheathed.I wish to replace the bulb holder with a replacement having an earth connection using three core wire.The bulb holder is screwed directly to the main body of the lamp which has a plastic switch to the base.Will this be sufficient or do I Also have to earth the lamp body also.
I have yet to establish if a thicker cable will run through the available space as it is quite restricted and wonder how others have overcome this