The Nationwide house price data suggests that property prices were 0.6% lower in August than in July, and 0.4% down on the same month last year.
The average home now costs £165,914.
Nationwide's chief economist Robert Gardner said.
"For some time now the residential property market has been moving sideways, as weak demand for homes co-existed with a situation where relatively few homes were coming on to the market, a further fall in employment would be likely to upset the relatively delicate demand-supply balance and put downward pressure on prices."
The most recently published Land Registry most recently published figures show prices fell by 8.8% in the North East of England in the year to July. There was also an annual drop in prices in every area of England and Wales, except London