The survey, commissioned by the Royal Commonwealth Society, suggests 70 per cent of Australians support the idea, giving the right to work and live freely in each nation.
Adults under age 35 were most in favour of EU-style free movement between the four countries.
Australia's High Commissioner to Britain, Alexander Downer, has told the ABC he cannot see the current system changing anytime soon, though, because of border-security issues.
"From Australia's point of view, we have a non-discriminatory policy in relation to visas and, for that matter, immigration. So, to come to Australia, everyone needs a visa, and, if we started exempting countries from that sort of arrangement, then that would create some complications and inconsistency for us, so I suspect, for many years to come, we'll stick to pretty much the system we have now, which, for Australians, is non-controversial. It means we can manage people coming to Australia, we know who's coming."
