HONDA JAZZ under warrenty - problem - dealer not helping

Hintza

What wheels and tyres does it have?

Very much sounds like tramlining as suggested.

bob_a_builder

we have a Jazz, well the wife does, its a bit older, an 04 one.

And ours might do the same, in our case I wouldn't call it un-nerving but did recognise it from your description. I don't drive it often and she doesn't drive it far or very fast.
I'd just put it down to the differences between cars, I often found similar effect when driving mondeos

as for "know about the problem and its a design fault",
don't think I saw anything like that is listed on Honest johns site regarding that when checking out Jazzs

Interested to see what you find out