Thanks for your help and suggestions, everyone. It seems that the it was the backlight itself at fault. As I commented earlier, pressing a certain point on the screen surround resulted in the screen going dim (at the bottom, just to the left of where it says 'macbook'). If I released the pressure (by removing the screen bezel or flexing the whole screen) I could set the brightness to minimum and then raise it to make light up again.
Firstly I replaced the screen inverter as it was the most likely culprit but there was no change. After reading around I suspected that the inverter cable had been damaged and was shorting so I purchased and replaced that but still the problem persisted. I replaced the screen last night and it has been working without problem since.
I suspect, though I haven't dismantled the screen to confirm it, that where the bulb connects to the power source has a problem. If I get the chance I'll test this.
Regards,
Andy