UK house price growth “almost ground to a halt” in September, with property prices 0.2% higher than a year ago, the Nationwide has said.
The building society also said that prices fell by 0.2% compared with August, according to figures based on its own mortgage data.
It said activity in the housing market had been slow, but stable, for two years.
The average home was now valued at £215,352, it said.
The year-on-year change in house prices is seen as the least volatile measure of the UK housing market.
Brexit uncertainty had widely been associated with the relatively static UK housing market, but some commentators have said this has led to pent-up demand.