1st Gen R53 Cooper S Knocking in suspension

I'd venture to say the strut top rubber has ripped and is separating from the bearing. Take a good look at them to make sure this is not the case. Also look at the strut tops for evidence of mushrooming. The 3 studs should all be pointing up from the strut top a 90 degree angle. If there is mushrooming they will point off center.

Good strut top with no mushrooming will have studs looking like |

Mushroomed strut top will have studs looking like / away from center.

 

I would also suspect the rubber strut top bushing. You can see it from the engine compartment. Look down the big hole where the shock rod comes into the engine compartment. There is a rubber mount around the shock rod. The rubber is probably ripped/torn.

 

^^^ These are the first things I would check.

Next Lower control arm bushings or a broken end link.