UK house prices have now recovered to the same level as a year ago, according to the latest Nationwide figures.
The average price of a home last month was equal to September 2008, it said.
The building society said that UK house prices rose by 0.9% in September compared with August, the fifth consecutive monthly increase.
Nationwide said the price rises suggested that the worst of the recession was over. But it warned the rate of price increases may now slow.
Remaining cautious
The average price of a UK home rose to £161,816 last month, up from £160,224 in August, the Nationwide said.
The three-month on three-month comparison of property prices - considered a less volatile measure than the monthly data - showed a rise of 3.8% in the three months to the end of September.
This was up from August's measure of 3.3% and was the biggest reported by the Nationwide since August 2004.
"The further increase in house prices is very much consistent with improvements in a broad range of economic and financial indicators over the last few months, all of which suggest that the most intense phase of the recession and financial crisis have probably passed," said the Nationwide's chief economist Martin Gahbauer.
However, he added that the housing market still faced "considerable headwinds", such as high unemployment and the continuing difficulty of getting a mortgage.
"It would be surprising to see house prices continuing to increase at the very strong rate seen in recent months," he said.
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.
While prospective first-time buyers have been helped by continuing low mortgage interest rates, lenders have been criticised for demanding large deposits, which are still preventing many from getting on the housing ladder.