1st response
'That sounds positively dangerous.
The only thing that came to mind was the front anti-roll bar bushes are knackered. This would cause all sorts of weird handling problems. I hope that it's this as it would be a simple, cheap fix. Get it checked out soon though.'
2nd response
'I reckon it's the diff actually
Before checking that though, it's worth checking to make sure the subframe is securely bolted to the bodyshell.......'
3rd response
'Quick way to check for engine mounts - get someone to sit in the car and rev the engine. If the engine lurches back and forth - engine mounts. My fiesta used to do that. I thought it was cool at first, then realised 2 of the mounts were badly damaged, and it was VERY not cool! '