Recent rises in UK interest rates are beginning to have an impact on homebuyers, the Nationwide has said.
A lack of supply will continue to support prices, Nationwide says
But the building society's housing survey still showed prices up by 0.7% in February, lifting annual price growth to 10.2% from 9.3% in January.
Nationwide said interest among buyers and demand for mortgages was beginning to wane following the rate increases.
Even so, it said price inflation would remain firm for a while, because of a lack of supply of properties for sale.
Nationwide said the average price of a UK property now stood at £174,706.
"Not all indicators are cooling just yet," said the Nationwide's chief economist, Fionnuala Earley.
"For now, supply issues are keeping an upward pressure on prices as property sales have continued to rise, while the number of properties placed on the market has been falling," she added.
The building society points to a recent dip in new mortgage approvals, and enquiries from would-be buyers at estate agents, as evidence that the market may be about to cool off in the wake of the Bank of England's three recent increases in interest rates.
On Tuesday, the British Bankers' Association reported that its members, who account for about half of current mortgage lending, had seen a small fall in new mortgages approved for home buyers in January, compared with the same month last year.
However, the Nationwide points out that the buy-to-let market is also keeping the wider property market buoyant.
Ms Earley admitted it might be some time before the annual rate of house price inflation started to subside.
"The annual rate of house price growth will remain close to 10% until late spring. By the second half of 2007, we continue to expect to see a more pronounced slowdown," she said.