House prices were "unseasonably strong" in September, shrugging off August's rate rise, the Nationwide says.
August's rate rise did nothing to deter buyers, the Nationwide says
The building society's housing survey found that prices rose by 1.3% during the month, lifting the annual rate of growth to 8.2%.
The gain - the fastest annual growth rate since February 2005 - means the average UK property now costs £169,413.
The three-monthly trend showed prices up 2.2% in the three months to September, on the previous quarter.
Demand in the housing market remained "firm", said Fionnuala Earley, Nationwide's group economist.
"Just like the weather, the housing market was unseasonably warm in September as August's interest rate hike did nothing to cool the rate of house price inflation," she said.
"Buyer interest remains robust as estate agents continue to report strong enquiries.
"However, fewer sellers willing to put their properties on the market is adding to already squeezed supply - which increases price pressure."
New mortgage approvals are still rising, indicating strong demand in the pipeline.
And the Nationwide also pointed to the continued activity of buy-to-let landlords as another factor keeping the market going.
This latest survey confounds widespread predictions that house prices would slow down as the year wore on, especially in the wake of August's rise in interest rates.
With the average house now costing - according to the Nationwide - nearly £13,000 more than at this time last year, house prices have continued to outstrip the increase in most peoples' take-home incomes.
The building society suggests that many first-time buyers are being helped to get a foot on the property ladder by their parents remortgaging their own properties to cash in on rising house prices and giving their offspring a deposit.
Each month almost as many people remortgage their homes - borrowing more while staying put - as borrow to actually move house.
The Nationwide calculates that when they do this they typically increase their mortgages by about 10%.
Doing so even on a house first bought just two years ago would typically raise an extra £11,500 per borrower, paying for most of an average first-time buyer's deposit.
Even so, the rising burden of mortgages, utility bills and an other possible rate rise in November - widely predicted by City economists - may eventually cool down the market.
"A growing number of people have missed mortgage payments recently," said Howard Archer of Global Insight.
"Even a relatively small overall increase in interest rates could ultimately have a clear dampening impact on housing market activity."