I have a 2001 XK8 with 93000 miles. It drives very well on smooth roads, however on a blacktop road with ruts it wants to wander. I checked all the bushings, tie rods and ball joints, they appear to be ok with the exception of the lower shock mount. I have some play in the lower bushing on the drivers side, none on the passenger side.
I am running 28psi on Pirelli tires. The car sits 3/4 inch low in the front. Alignment was done 10000 miles ago.
Could worn upper shock mount and worn lower shock bushing cause my problem? I read somewhere that worn upper shock mounts cause the car to sit lower in the front. Also the bolt and nut that is on top of the strut is not centered in shock tower.

 

Barring anything mechanical, the wide tires on these beasties do have a tendency to grab onto any linear tracks on the road, it's called tramlining.

 

Check rear hubs. After having rear wheel bearing replaced on the driver side, I got on the freeway and each time I accelerated. it felt like the rear end was trying to wrap around to the front, positively frightening. It wouldn't happen at low speeds but at freeway speeds or upon accelearation. Damaged wheel hub was the problem; very dangerous.

 

From your description the top shock mounts are shot - fairly common fault. That will alter the camber angle which could affect the steering in the manner you describe.