My 1997 convertible centre dash with the AC Buttons, heated rear and front screens fog lights switches etc no longer illuminate with the lights turned on can anyone help? The rest of the dash do and they dim with the dimmer switch.

 

Check to see if all your exterior lights are still working. I had an issue like this with a 98 XJ8. The electrics are very similar on the XK as well. The fault was a couple of wires had fallen off the rear of the light switch on the steering column. The soldering was not good and had just come off due to the vibration up the column.
You will need to power down the car's electrical system to prevent the airbag from activating before you remove the steering wheel and the switch. Turn the switch over to see the connections. Hope this helps.