Hi Peter !
Is the transformer dead or just the power switch ?
Try to figure out by measuring the voltage arriving at the transformer, after the switch. It is somewhat unusual for a transformer to die, unless it is so badly enginereed that it became a heater....
If by any chance, it is dead, go to any electronic shop and ask for a toroidal 12 V transformer (primary is your mains voltage here 230 V and secondary is 12 V) when asked for rating give them the power of the bulb you use, form memory, 100 W. You will get an ever lasting unit and of very good quality for a few pounds.
Please keep in mind that electricity is a dangerous and lethal thing if not handled properly ! So if you do not feel capable of handling this repair, keep it to a porfessional ! Life is so short !