I've not had it, but it sounds very much like it. The logical cure is a steering damper, see details on the Gomog website.
http://www.gomog.com/allmorgan2.html

Also a kit from Mulberry Fabrications:
http://www.mulfab.co.uk/our-products/8/steering-suspension/steering-damper

I'm sure others more knowledgeable re this problem will be along soon!

Nigel