Prices in the latest three months (July-September) were 2.0% higher than in the preceding three months.
The average home in the UK stood at £202,859 in September – down 0.9% from August.
Martin Ellis, Halifax housing economist, said: “Housing demand has been strengthening recently, underpinned by economic growth, rising real earnings and very low mortgage rates.
“Increasing demand is combining with very low supply to drive robust underlying house price growth. There is little reason to expect any fundamental shift in the key market drivers over the coming months.”
Ed Stansfield, chief property economist at Capital Economics, said: "Average house prices in the UK fell by 0.9% during September. But we would not read anything into that drop.
"After all, the Halifax tends to be the most volatile of the major house price indices, and this month’s dip needs to be seen as a partial unwinding of August’s 2.7% m/m rise. Nevertheless, the more stable 3m/3m growth rate did slow to 2% in September, down from a recent high of 3.3% in June, implying that on this measure at least, the pressure on prices has eased a little over the summer.
"House price growth should remain solid in the final stages of the year, as the recovery in average incomes and consumer confidence boosts demand, increasing the competition among buyers for the limited supply of homes for sale.
"Accordingly, while house price growth on the Halifax measure might ease back a touch, the other measures will probably pick-up so that the major indices will all show a rise in house prices of between 5% and 7% for 2015."