It happens that Mad Cow formulated :

The flowers are Alstroemeria (your description of the habit of growth
was spot-on too) but seemed more like A. psittacina than A.
brasiliensis.

Ah, thank you so much for that, indeed that is what it is.
Now I know, I will dig some of them up and put them in a better place
and look after them. :-) This is the first time they have flowered
since we've owned the land and I never really bothered to look after
them, I certainly will now. :-)
Thanks!

--
Barbara

http://www.flickr.com/photos/barbara-h/