“All Anglepoise lamps are designed and tested as Class II or double insulated electrical appliances, which means they have been designed in such a way that they do not require a safety connection to electrical earth (ground).
The basic legal requirement is that no single failure can result in dangerous voltage becoming exposed so that it might cause an electric shock and that this is achieved without relying on an earthed metal casing. This is achieved by having two layers of insulating material surrounding live parts or by using reinforced insulation. Hence the outer material can be metal as the risk of becoming live is negligible (many household products are similar).
All Anglepoise lamps bear the double insulation symbol (a square inside another square).
References: Directive 2006/95/EC – Harmonisation of the laws of Member States relating to electrical equipment designed for use within certain voltage limits; IEC 61140: Protection against electric shock — Common aspects for installation and equipment. 2001; BS 2754 : 1976 (1999): Memorandum. Construction of electrical equipment for protection against electric shock.”
However this is only true if you have not fitted a metal bulb holder, then you must have an earth wire. I have lots of emails from people on this subject so take earthing into account when planning your restoration.