The latest data from Nationwide joins a raft of evidence pointing to the country’s housing market stagnating over the summer.
The average house price now stands at just over £166,500.
According to Nationwide, the annual rate of price inflation has slipped to 3.9%, down from 6.6% in July and from 8.7% in June.
The 3-month comparative change in prices – generally seen as a smoother indicator of house price trends – fell from 1.2% in July to 0% in August.
Martin Gahbauer, Nationwide’s Chief Economist, said: “Unless prices bounce back in September, the three-month rate of change will turn negative next month.
He added: “Recent market trends remain consistent with an unwinding of the supply-demand imbalance that drove up prices for much of the last year.
“As more sellers have returned to the market, buyers have a greater selection of properties to choose from and more bargaining power with which to bid down asking prices.”