House prices barely moved last month, shedding a fractional gain recorded in July and going back to precisely where they were in June, according to Nationwide.
But because the relatively buoyant month of August last year dropped out of the 12-months, the year-on-year increase fell back to 2.3 per cent, its lowest for nine years.
The average price of £157,310 is £1,038 down in July, but still higher than in May.
"In spite of a fair deal of bearish comment, the housing market has remained quite resilient this year following last year's interest rate hikes," said Fionnuala Earley, Nationwide's economist.
"House prices increased in eight out of the last 12 months, but the general path of house price inflation continues to be soft.
"Price inflation has slowed gradually, but is still positive, and activity has been creeping up since the end of 2004."
She pointed out that some 97,000 mortgages for homebuyers were approved last month - more than in August last year.
But while activity in the housing market seems to have stabilised, she warned that this did not signal the start of a further period of sustained growth in house prices.
Nationwide noted that although pay is rising almost twice as fast as house prices, affordability is still an issue, particularly for first-time buyers.
The ratio of house prices to the earnings of people trying to buy their first home is considerably higher than during the last peak of the housing market.
Average first-time buyers can now expect mortgage repayments to take up a third of their take-home pay, the building society added.
They would need a deposit of nearly £17,000, compared with about £11,000 in 2003, she said.
Nationwide also warned that now consumer debt has passed the £1 trillion mark, households are more vulnerable to changes in the economy.
Ms Earley said: "The current background suggests that the market will continue to cool in a contained fashion.
"But it will be some time before we can expect prices and activity to return to the growth rates seen in the last two years.
"Lower interest rates are a reflection of lower inflation and while lower rates mean that borrowers can afford to service higher levels of debt, lower inflation means that it takes longer for the real value of that debt to erode.
"We can therefore expect a sustained period of unexciting movements in house prices before consumers' financial balance sheets are restored to more comfortable levels."