Early stage of some insect? - looks like a collage of dried bark and sticks, hair etc!!
I gently squeezed the top of one, and it looked like a fly type of creature?
Recent photos 1 & 2 lying on a cushion in my sunroom.
Photo 3 on internal garage wall.
Photo 4 the underneath
There are at least two possibilities here - one is a caterpillar in the family Tineidae such as the household casebearer - http://resizing.info/openphoto.php?img=http://pestweb.com/assets/images/pests/600/LM58_01.jpg
The other would be a caterpillar in the family Psychidae (bagworms) - http://www.terrain.net.nz/friends-of-te-henui-group/caterpillars/caterpillar-of-the-common-bag-moth-liothula-omnivore-liothula-omnivore.html
Thank you Flapdoodle - you set me on the right track!
Australian Bagmoth (Cebysa leucotelus)
http://www.terrain.net.nz/friends-of-te-henui-group/moths/cebysa-leucotelus-australian-bagmoth.html
