I spoke with both Adrian and Graham on Friday when they popped round with both +8s and the tyres swapped. It would appear that the Adrian's tyres were far superior and proved that Graham's 10+ year old tyres were in need of replacement. Although they look ok, it seems that the tyres harden out and can cause steering and road holding problems. The shimmy had disappeared.
Neil
I think the result shows that tyres (and/or wheels) can be the cause - it did in my case. I can also imagine that certain types could generate a greater effect than others.
Even if perhaps a bit premature, I think there is a pattern emerging: The shimmy itself is not caused by imperfections in the construction but by imperfections in tyres and rims (as well as all other parts involved). On the other hand I believe that the delicate lightweight construction is more sensitive to uneven or unbalanced tyres/wheels than modern car's.
For this reason I have fitted a steering damper and will also fit 'brake reaction bars' - even though my shimmy is completely gone since I fitted two new rims in front.