Wiring - 230V on a 120V 18/2 wire?
The cable is not the problem.  It takes less current to supply the same power at 240 V as it does at 120 V.  The wires intended for 120 V operation therefore have excess current capability.

However, you have to consider voltage on other parts.  The switch has to withstand more voltage when open, and so does the insulation between you and the high voltage.  Probably both of these can handle the extra voltage.  However, if something happens, the liability is on you.  If the lamp catches fire and burns the house down, the insurance company would have a legitimate reason not to pay.  If someone got electrocuted by touching this lamp, you could be in serious trouble.

All around, this is a bad idea.  Leave the US lamp in the US.  Get a UK lamp for use in the UK.