Lithgow "H" barrel? Not sure of vintage, probably post WW2 as it is still greased up and in a long plastic bag.
The No4 7.62 barrels are marked "A W", an inch or so forward of the Knox Form. and a lightly-struck "crown over crossed pennants" on the left side of the Knox Form. They are a dark grey Parkerized finish, and have foresight mounting lugs, but NO bayonet lugs. Thus, not L8 /"military" barrels and probably made in the early 1960's, specifically for the Civilian range trade.. Definitely 1:12", 6-groove, RH twist, with narrow lands like an L1A1 barrel and the extractor "notch" is cut a couple of millimeters further forward than on a .303 barrel.
I scored them over twenty years ago and, by the minor scuff marks on the outer surface, they had been rattling around, out of any possible "factory" plastic bag and preservative coating for quite a while before I got them.
I have seen another with a different code; "A X", I think. That may indicate a "year code" as stamped on L1A1 barrels, but I do not know for certain.
Just checked my notes: If you have a "real" Oz L1A1 barrel that is marked BCF: the "B" indicates six-groove rifling and the CF indicates "Cold" (Hammer) Forging". That's all I have at the moment.