The average property price now stands at £202,859, down from £204,722 in August.
On an annual basis, house price growth eased to 8.6% in the three months to September, down from 9% in August.
On a quarterly basis, prices in the latest three months (July-September) were 2.0% higher than in the preceding three months (April-June).
The quarterly rate of change fell from August’s 3.0%, to 2.1%, its lowest since May.
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.”
Mortgage approvals increased for the third successive month in August. The volume of house purchase approvals – a leading indicator of completed house sales – increased by 3% in August to the highest level since January 2014.
Approvals in the three months to August were 6% higher than in the preceding three months (March- May) and 6% higher than in the same three months last year.
Meanwhile, separate research by Halifax found that flat prices have outpaced house prices over the past decade.
There has been a 60% increase in the average price of a flat over the past ten years, significantly higher than the 38% rise for all residential properties. Detached homes (21%) and bungalows (28%) have recorded the smallest rises over the last decade.