UK house prices rose by 0.1% in September compared with August, according to data published by the Halifax, based on its own lending figures.
However, the lender warned that the month figure should not mask a "steady downward trend" noted over the past six months. Halifax said, if measured on a three-month basis, house prices fell by 0.1% in the three months to the end of September, compared with the previous quarter.
Martin Ellis, economist at the Halifax, said year-on-year, house prices were still rising albeit at a slower pace.
"Prices rose by 5.8% in September compared with a year ago. The housing market has followed a steady downward trend over the past six months with clear evidence of both a softening in activity levels and an easing in house price inflation."
Ellis added that house prices were still rising faster than earnings for some, which was in effect behind the reduced demand from buyers.
In an earlier assessment, Halifax's rival lender the Nationwide Building Society said annual house price inflation had fallen to 5.3% in September from 5.6% in August.