I think this might be Straw flycap (Amanita australis). It seems to fit the descriptions quite well. Although it was growing in oak dominated forest at Victoria Park, there was also a lot of kanuka and manuka around which I believe to be two of the native species this fungi associates with.
upper terrace scarp under elm tree in mown grass and leaf litter; Oxford Tce; elm tree entered as well for ID
variety spica - ID by Jerry Cooper; in mown shaded grass and leaf litter under oak (Q robur) in parkland