The price of a typical house increasing by 0.9% on a seasonally adjusted basis, according to the Nationwide building society.

This means that house prices are now at the same level as September last year.

The three-month on three-month rate of change – generally a smoother indicator of the near term trend – rose from 3.3% in August to 3.8% in September, the highest level since August 2004.

At £161,816, the average price of a typical UK property was essentially unchanged from a year earlier, representing the first time since March 2008 that the year-on-year rate of change has not been negative.

Over the first nine months of 2009, the seasonally adjusted index of house prices has risen by 4.1%, though relative to the October 2007 peak it is still down by 13.5%.

Martin Gahbauer, Nationwide’s chief economist, said: “One reason to remain cautious about the outlook for house prices is that turnover in the market is still well below normal levels. The housing turnover rate – measuring the percentage of the private sector housing stock changing hands on an annualised basis – fell to only 3% at the end of 2008. Although it has since recovered to nearly 4%