Have to check - but I think Wackett (CAC) had no interest whatsoever in the P.1081. Sabre all the way.
That's right. While the Brits and the Aussie government were ironing out the projected fighter based on the P.1052, Wackett was doing a sneaky and was in secret talks with North American about the possibility of building the Sabre, but powered by the AJ.65 (Avon). Despite going behind everyone's backs, Wackett had support from the RAAF head and apparently made a convincing enough argument to the government to go for the Sabre. In fact, the deal was almost concrete in 1949, especially when Hives of RR got behind the idea of putting an Avon into the Sabre - and this was before the P.1081 had even flown for the first time. Wackett did happen to propose a slightly unrealistic manufacturing and in-service date, though, which can't have done his case any harm in the eyes of NAA and RR.
Despite the growing interest in the Avon Sabre, the P.1081 still held official interest in Australia, but its end boils down to a lack of faith in the aircraft and engine combination by the British. The P.1081 was to be fitted with the Tay, but the Aussies wanted a reheated Nene, but since neither the airframe nor engine received any great priority, therefore support from Britain the project was cancelled in late 1950.