There has been a lot written about shimmy, and some of it is true!
I have one bike, a Mercian, that this can happen on.....if I either remove one hand from the bars (scary!) or place one thigh against the top tube, it will stop.
Funnily enough, if I have the front end loaded, it doesn't do it.
The best bit I read on t'internet was about some sort of 'triangulation' type theory.....can't find it, or explain it properly right now!