Real Video: Hayley Miller reports on the autumn house selling season

The Nationwide said that on a month-to-month basis house prices fell by 0.2% in September, slightly less than the 0.5% drop that was seen in August.

The slowdown in the wider economy is hitting house prices

But on a year-on-year basis property prices are still sharply up, 7.5% higher than this time last year, although the price rises are slowing down.

Paul Sanderson, Nationwide's head of research, said: "The fall in prices recorded in September was slight, but after August's decline this should be seen as further evidence of changing market conditions.

"Buyer demand has clearly weakened over recent months, although a softer trend in prices may have been reinforced by a modest increase in properties coming on to the market."

South East hardest hit

He added that this slowdown had been expected, and had been led by a drop in house prices in the South East and London.

Other house price surveys also indicate that property inflation is slowing down, and in some cases house prices are declining on a monthly basis.

Estate agents say it is not the start of a housing recession but a slowdown

But most commentators agree that this does not signal a housing recession.

House prices should continue to grow, but at a more modest rate.

Mr Sanderson said that activity in the housing market was expected to remain reasonably resilient.

But he added: "It will not be immune to the inevitable slowing in the wider economy already under way. House price inflation is likely to continue to ease, with sales levels remaining at best flat, well into next year."