Thanks for the replies. It has certainly given me some food for thought.
I can confirm that the pitot heat was tested pre-flight and selected "on" before departure ... but I suppose that is no guarantee that it was functioning at the time of the occurence. I don't recall checking the circuit breakers during or afterwards - I don't know if my instructor did - we were both pretty shaken.
There was no visible airframe ice and the OAT was above freezing.
The idea of self induced problems had not crossed my mind, but thinking of experiences in my day job (as a consultant/programme manager of complex projects) problems are often caused by human error (usually a number of small, yet critical, oversights or porr decisions.)
It is human nature to be defensive and look for external causes, when in fact the reality is closer to home.
The counter balance to this view is that it was a training flight and I had an instructor fresh from an IR monitoring me closely from the RHS - of course, it could have been a joint screw up!
Finally, the ASI reading zero was transient. I am note sure how long the incident lasted for, but it could not have been too long, as we "only" gained about 1100' with VSI against the up stop. As soon as we hit the little bump and the VSI reversed, the ASI shot up from zero to over 100KTS in seconds. The a/c was a PA28-140 by the way, don't know if this is significant.