There are two schools of thought. One is that things have sorted themselves out and boom-and-bust is unlikely to be repeated. The other is that the Government needs new policies now to guard against the danger.
Surveys show British attachment to the idea of home ownership remains firm and there is also plenty of long- term demand for extra homes.
The Government estimates that the number of English households is likely to grow by almost three million in the next 20 years; roughly equivalent to the total number of homes in London.
This growth is fuelled by a population which is still slowly expanding and the strong trend towards smaller households caused by rising numbers of the divorced, single-parent families and elderly, widowed people.
But most analysts think a repeat of the damaging Eighties boom, when prices doubled in less than six years, is unlikely. Future borrowers and lenders are likely to be more prudent.
'They know that house prices are no longer a one-way bet,' said Bob Pannell of the Association of Mortgage Lenders, which represents the banks and building societies. Mr Pannell believes that if the market overheated once again the Government would call lenders in 'for tea and sandwiches' and tell them it had to stop, through voluntary restraints on their lending. Ministers will be loath to use drastic increases in interest rates to damp down house price inflation because of their damaging effect on the economy.
They have three other main options for trying to preserve the gains in affordability and prevent another boom-and-bust.
They can end tax relief on mortgage interest, which will cost the Government about pounds 9bn in lost revenue the next financial year.
By in effect making mortgages cost more, removing the subsidy would reduce house prices - by up to 9 per cent according to a study for the Joseph Rowntree Foundation. But phasing in the removal over several years when house prices were rising should act as a stabiliser rather than a depressant.
The huge savings to government would allow it to cut income tax and interest rates, which would counterbalance any deflation caused by removing the subsidy. According to the Joseph Rowntree study, first-time buyers would gain more from lower interest rates and cheaper houses than they would lose from ending the tax relief.
Phasing it out would also allow the Government to focus subsidies on low earning home-owners who really need them.
They are at a disadvantage compared to low-earning home renters, who can qualify for housing benefit. Home-owners only get state help with their mortgage repayments if they are unemployed. Those who lose a job are sometimes discouraged from taking lower-paid work because it would mean a drop in their total income; they are caught in a poverty trap.
Another option for holding down house prices is to stimulate private renting, giving people a reasonable option not to buy. The number of people renting privately has been declining for decades but has revived in the past few years, especially in the South-east.
One reason for the turnaround is that home-owners who cannot sell and need to move have gone into rented accommodation and put their own houses out to let. The other is that the Government, belatedly recognising that some alternative was needed to home ownership and social housing, brought in a series of initiatives and laws to encourage landlords.
But the recovery in renting is weak and may not last once house prices stabilise. John Muellbauer argues that now is the time for extra measures to encourage landlords, because they can buy houses at low prices, both boosting the rental sector and helping to stabilise the market. He wants capital gains tax for landlords abolished or reduced sharply, and for them to be able to claim tax relief for depreciation of their property.
Building new houses to meet the underlying long-term demand would also help to prevent another price upheaval. The Federation of House Builders claims that problems in getting planning permission from councils for new homes in the Home Counties and other rural areas was one of the main reasons for soaring house prices in the 1980s.
Few observers accept the association's view that simply building more private houses is the answer, but if more land were available house prices could be kept down. At present the cost of land accounts for about 40 per cent of the average new home's price.