The clicking noise could be the ABS system activating at low speeds. It feels like pulsating or shaking from the brake pedal. If the ABS is activating at low speeds then most likely one (or more) of the speed sensors is loosing connectivity with the ABS module (dirt or faulty sensor) causing the ABS system to activate.

Had a similar issue on my 00 S Type - the RH front hub assembly was shot causing grease and metal fragments to coat the speed sensor causing loss of signal to the ABS module - activating the ABS system everytime I stepped on the brake pedal to stop.

 

When new pads are installed an anti-rattle clip is installed in the caliper to keep the pads from rattling back and forth under braking as they are pressed against the rotor. It's possible that you have one that has been damaged or was not installed properly with your last pad installation. Try to see if the rattle or click is coming from one particular corner(s) and remove that wheel(s) and see if the pads are loose in their mounts. If they are then you've got a clip missing or displaced/damaged.

 

Thanks all for the input, I'll check it as soon as I can.