The Economist's global house price comparison suggests that UK residential property is 34% overpriced and Australian property 61% overpriced. Jeremy Grantham looked at 34 historical asset bubbles, of which 2 remain unburst - the Australian and UK housing markets. In the Demographia metropolitan market affordability rankings (PDF), Australian cities take six of the bottom ten places, with median multiples from 7.4 to 9.1, while London and significant numbers of other UK areas are over 6.
On any formal metrics - the Economist used price-to-rent ratios, Grantham used deviations from long-term trends in price-to-income ratios, Demographia uses median price to median income ratios - it's clear that Australian and UK house prices are at or near all time highs. Reversion to historical values for these metrics is not a certainty, but given comparisons both with other countries and historically within the UK and Australia (e.g. the 1890s), there has to be a good chance that prices will return, at some point in the future, to historically normal levels. (Grantham: "it would be the first time in history that such a bubble has not broken".)
House prices are now driven largely by the availability of credit, so they are most sensitive to interest rates and required loan-to-valuation ratios. And the ability of the private sector to increase debt levels seems limited. The following graph (taken from Steve Keen) provides some historical context here.
I find none of the counterarguments to the likelihood of a crash or at least a correction at all convincing, especially given the events of the last few years and a comparative perspective. Many places have worse housing shortages (and Australia's ratio of people to houses has actually been dropping, not increasing). Long term demographic trends such as the shift to two-income households are also present in Spain and Ireland and the United States. Finance and tax advantages for housing are also widespread - in the US, mortgages are typically fixed for thirty or forty years, and mortgage payments by owner-occupiers are tax deductible.
Which will go first?
Judging by the areas I've looked at first hand, rental yields in Oxford are definitely higher than in Sydney - gross yields up around 5% instead of well under 4%. So the Economist numbers seem right to me: the Australian bubble is bigger.
However the Australian economy is steaming along just fine, while the UK has higher unemployment and is braced for massive cuts to the public sector, with accompanying redundancies. The Australian government also has less debt, giving it more room to bail out the private sector in the event of further financial shocks. And the devaluation of the pound has already lowered effective house prices for foreign buyers (most citizens of the EU have the right to live in the UK and buy property here) and locals with foreign assets.
It's hard to see anything rapid happening in Australia, barring sudden shocks from China. On the other hand, the banks' cost of funding is likely to increase, even without RBA interest rate moves, and they are unlikely to go back to 95% loans, making it hard to see how significant further house price rises can happen. But even flat house prices for any extended period of time will make negatively-geared investors (about two thirds of them!) unhappy, so the ponzi part of the bubble has to unwind eventually...
As Keynes is supposed to have said, "markets can remain irrational longer than you can remain solvent", so I'm not about to short the Australian banks (or even go short CBA and WBC and long ANZ and NAB, which would be a safer approach). I am, however, keeping my hands out of the FIRE.