In a latest sign of the slowdown in Britain's housing market since last year's Brexit vote, Nationwide said prices in London fell by an annual 0.6 percent this month.
The British capital - which has attracted property investors around the world - represented the weakest performing region in the country for the first time since 2005.
Nationally, Nationwide said house prices rose 2.0 percent year-on-year in September, slowing slightly from a rise of 2.1 percent in August and the weakest increase since June 2013.
A Reuters poll of economists had pointed to annual growth of 1.9 percent for house prices across Britain.
Nationwide said pressure on household incomes, caused by rising inflation and slow wage growth, was cancelling out some of the support for the market from rock-bottom interest rates.
The Bank of England is widely expected to raise rates soon, possibly as soon as Nov. 2 at the end of its next policy meeting. But Nationwide said a modest rise by the BoE would probably have only a small impact.
"This is partly because the proportion of borrowers directly impacted will be smaller than in the past. In recent years the vast majority of new mortgages have been extended on fixed interest rates," Nationwide Chief Economist Robert Gardner said.
British house prices were rising by more than 5 percent a year at the time of last year's referendum decision by voters to leave the European Union, according to Nationwide's index, almost three times the current pace of growth.
In month-on-month terms, British house prices rose by 0.2 percent in September after falling by 0.1 percent in August.
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