House prices edged up 0.5% to stand at £189,333 this month, Nationwide has reported.
Annual house price inflation is now 9%, said the lender.
Despite the rises, Nationwide said that the housing market is losing momentum, with annual house price inflation slipping from 9.4% in September.
It also said that mortgage approvals for house purchase in September were almost 20% below the number approved in January.
Separately, the NAEA said that in September, demand was at a near ten-year high, while supply was at a 12-year low.
It said the number of applicants last month was the highest in nearly ten years, but that while supply rose, the increase was so tiny as to be a 12-year low for the month.
The NAEA said the average branch had 406 applicants with 49 properties available.
Despite the mismatch, the large majority of homes (82%) exchanged at under the asking price.
