At some point the brake lights failed. No idea when as it is not something you see as a driver. After some investigation it appeared the switch was the cause. When I took it apart it was burnt and corroded inside. Apparently not unusual.
This is the location of the switch, just in front of the brake pedal.
Pressing the brake pedal closes the switch and turns the lights on.
I couldn't find a replacement but did find one from a Mini on E-Bay at 99p.
But fitting it on showed a problem. The brake lights were permanently on. Turns out that whereas the original was a 'push-to-make' switch, this one was a 'push-to-break' switch.
But rather than try and find another replacement I simply fabricated a new mounting bracket from a stainless steel offcut and mounted it behind the brake pedal instead of the front, adjusting it so that it was pushed close when the brake pedal was in the normal position.
Very pleased with myself for lateral thinking !!