A tiny bit of hardwired dedicated logic integrated into the camera module would be more than adequate to do this - just gating of either the digital I/O or the power to the camera, and a pulse-stretcher so the LED goes on for at least a few seconds each time to prevent an attack by rapidly flicking the camera logic on and off.
A similar circuit for the microphone with a different-coloured physical LED - not just a software-controlled dot on the screen - would be a good idea too.