The Nationwide warned that the recent house price increases were unlikely to continue at their present rate, especially if more properties come on to the market.
"The most intense phase of the recession and financial crisis has probably passed," said Martin Gahbauer, the Nationwide's chief economist.
"However, given that the housing market still faces considerable headwinds in the form of high unemployment, restrictive credit conditions and an impending withdrawal of the stamp duty holiday, it would be surprising to see house prices continuing to increase at the very strong rate seen in recent months," he added.
Figures from the financial information company Moneyfacts show that mortgage rationing is still in full force.
The number of mortgage deals available with between 0% and 40% deposits rose by just 4 in the last month, to 1,290.
Of these, the proportion requiring at least a 25% deposit has gone up up from 64% to 66%.
By contrast, as late as December last year, only 43% of the deals needed such a large down payment.
In addition, there were still 402 mortgage offers that needed only a 10% deposit - now there are just 101.
The Nationwide said price rises had been particularly vigorous in the past few months.
In the three months to September they rose by 3.8% compared to the average level in the previous three months - the biggest rise on this measure since August 2004.
The more fundamental reason why prices might start falling again is that, by most measures, they are still significantly over-valued
Mr Gahbauer said another reason to remain cautious about the outlook for house prices was that turnover in the market was still well below normal levels.
The Nationwide calculates that housing turnover - the percentage of private sector housing stock changing hands on an annualised basis - now stands at almost 4%.
This is still significantly lower than the rate of between 7% and 8% recorded before the downturn in the housing market.
David Smith, of property consultancy Carter Jonas, said anyone hoping to sell now had a "window of opportunity" that might soon shut.
"We have to expect more turbulence ahead, specifically as a result of rising unemployment and interest rates," he said.
"This toxic combination will bring more property on to the market as people struggle to meet their repayments, which will apply downward pressure on prices and potentially reverse the recent trend, at least for a time," he added.
Another factor that might depress house prices again would be if "accidental landlords" now decided to sell their homes instead of letting them to tenants, the Nationwide said.
"The downturn in housing turnover over the last two years has prompted many home movers to let their old properties out rather than sell," said Mr Gahbauer.
"The surge in so-called 'accidental landlords' has limited the supply of property in the sales market and increased the stock of homes available to let.
"Over recent months the increase in 'accidental landlords' seems to have tapered off, which may indicate that some of this elevated rental supply is returning to the sales market, with possible negative implications for house prices," he said.
The Royal Institution of Chartered Surveyors (Rics) agreed.
"The recent turnaround has been surprisingly strong," said Brigid O'Leary, an economist at Rics.
"An increase in property for sale would improve transaction levels but could also put some renewed downward pressure on house prices," she added.
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