I can only put in this link. If your plants have leaves like these it is not a native orchid,
A very good description of the Renga Reanga.
The plants have finished flowering, can you post a pic of yours on the Gallery.
Heather

Here is a link that might be useful: Arthropodium

I've had a closer look at the plant, and the text descriptions of a Renga Renga's base (clumping, like a flax)don't match my plant.
However, the plant does match the description of a Cattleya orchid. Are there any NZ native cattleyas? I can't even think of where else to look!?

Try this link, scroll down a the left side below journals and there are some pic links.
Heather

Here is a link that might be useful: NZ Orchids

Thank you for the link - I had no idea NZ orchids are so diverse. But after careful reading and looking at pic's, I think I can say for sure that my neighbour got it wrong. My plants are orchids - cattleyas, I'm also sure - but NOT native.
They are in the bed beneath a red gum, now, with the three identified Renga Rengas in a group, my plants in another group, separated by clumps of decorative grasses. I have a pic of my bloom, but the white glare makes it difficult to clearly see the structure. So I will put up a new photo as soon as I get better photos taken and scanned.
(Note to self: don't use flash when face-on to the white bloom!)

Thanks for all the input.

It's the "glary" photo, sorry but I can't get to a camera for a while.

Very definitely a crested iris, most likely I. japonica (not to be confused with Japanese iris I. ensata)
cheers, Jan who grows them in Oz.