OK I've narrowed the proposed replacement down to an LED 240-12v transformer - either with the original Anchorn AET3202CL or similar (dimensions of 7cm diameter circular 2cm deep, with a 9mm hole down the centre), or a small LCD transformer of any shape that will fit in the dome of the lamp. I already bought a rectangular one on Amazon that would have fitted if they hadn't got the dimensions wrong. Now trying eBay.