Claying a car removes only surface contaminants - not oxidised paint.
The easiest to get hold of (as Helfraiuds sell it) is Meguiars clay kit, but the best (in my view, as it only needs water as a lubricant) is Bilt Hamber clay, available at very few outlets, but is around a tenner online.
Think your paintwork is smooth? Think again! When you've shampoo'd and rinsed the car, rub a piece of clay over the paintwork and you'll be amazed at the cr*p it removes and the finish afterwords is like glass.
You'll need to lube the area (never use it dry) and then rinse off the residue, so it's a bit of a faff, but is totally worth it.
Cheers,
Mike