I've never had a whiteboard session, these type of interviews are not common in the non-start-up world in the UK. I just get really, really stressed in an interview.

To make matters worse, it seems that I project this aura of calm and self assurance, or so I've been told by two of my interviewers after they hired me, so that I don't even get a concession for obvious nervousness.

I do this as well. But it's not a few bad whiteboard sessions. The vast majority of whiteboard interviews are strictly adversarial.