Not Suillus which has pores on the underside, this has obvious gills. In this area I've only ever encountered Suillus in association with some exotic conifers (Pinaceae) so you are not going to see Suillus at the ANBG. It appears to have rust brown spores which excludes Armillaria and together with its size and the apparent surface texture of the cap it appears to be Gymnopilus junonius. Presumably this is in a well watered section of the gardens for it to be fruiting at the moment.