Nationwide warns that unless more homes come on the market, buyers will be stretched to afford to move.
But while prices continue to race ahead, the Bank of England reports that there was a fall, for the second month in a row, in the number of house-hunters approved for a mortgage.
Approvals had been revitalised over the winter, partly because of the government's Help to Buy scheme.
More recently, though, there may have been an early impact from stricter rules on mortgage applications -- which were launched officially last weekend, but imposed gradually by lenders over several months.
March saw just over 67,000 mortgages approved for house buyers, a reduction of more than 2,000 compared with February, and still around half the peak levels which were reached before the financial crisis.
Now I discover that while the Bank's seasonally adjusted figures show falls in mortgage approvals in February and March, their actual figures show increases both times!
In fact, there has been a year-on-year rise in approvals every month for the last 12 months...
So there may well be an impact from tougher mortgage application rules, but it probably isn't in the stats yet.