Hi Chriss, the image below is from a Monart dual lamp fitting, which is a type of fitting that will possibly do for your lamp.
Or alternatively you could get one made with new parts (the link below) from this company.http://www.lampsandlights.co.uk/table_lamp_kits.php
I have made two dual fittings for two of my own Monart lamps and one for board member Roberta.
The problem with old original lamp fittings they were not earthed ie. two core (electrician's hat) and cannot be used safely. Nowadays all metal lamp holders must be three core.