Hi Pete,
Can you clarify what you mean by a rear Anti Sway Bar, do you mean the radius arm, which is sort of triangular, with a large round hole at one end and a smaller round hole, at 90 degrees to the first, at the other? My understanding of a sway bar would be an anti Roll bar, which weren't standard on Series III cars. Terminology in different countries differs for many components.
An image of a radius arm can be found here (copy and paste the whole next line into your browser):
http://www.sngbarratt.com/catalogue/par ... eys=radius arm&modelfamilyid=&categoryid=&stype=1&pagepos=12&back=y&next=y
If so, then any E-Type Radius arm will fit, but early cars have mountings for roll bars, however the geometry is the same. I actually have one of each on my Series III, as that's how I got the car. You just don't use the roll bar mountings.
The radius arms from the S-Type (original 1960s car) or 420 fit too, according to that advert, which might make your search easier. They shouldn't be too hard to find and I think the one listed at SNG in the above post is quite good value, since it appears to include both bushes, which from SNG will be good quality, you could order the replacements for your other arm too. Postage from SNG is quite quick to Aus, so probably is to NZ too, but the arms are heavy and postage might be a little steep.
Now I am not sure about this, but if you check the other radius arms on the site, they list the later XJ6/12 and XJS arms as suitable for E-Type as well, if the dimensions are the same, they will fit and this might be a way to upgrade, better yet, any old XJ6/12 or XJS in a wreckers yard can donate a cheap pair, but you still need new bushes. However, give SNG a call first, or see if others on the forum know whether they fit the E-Type too.
As to availability of s/h originals, I have no idea of stockists in NZ, but I have an advert in my hands for the Jag E-Type Warehouse, phone no. +61 3 5156 7727, mobile +61 408388656. He used to be in Kinglake Victoria, prior to the bushfires of 2009. I have never been there or even spoken to him, he may no longer exist, but he says he has new, reconditioned, imported and used spares in the advert. He is now based in Newlands Arm, Victoria although my advert is in an old magazine (Oct 2009).
Incidentally, don't buy cheap bushes, I did and they tore before the car rolled more than 20 metres, I now have new genuine Melalastic bushes fitted.
Regards and good luck,