XJR 97 shaking/juddering steering and braking

[nitramshirley]

74,000 miles, '97 XJR. The steering shudders quite perceptibly and consistently on marginaly bumpy road surfaces. At first I thought this was just due to the large wheel surfaces and taught ride, but now I am convinced it is either a shock-absorber problem, or a steering flaw. I have read elsewhere that the shuddering - which seems more severe when I brake - may be caused by faulty brake calipers. I have pretty new tyres and have balanced the wheels recently... so I don't think that those are the cause. Any suggestions before I take her to a dealer?