Halifax says house prices have fallen for the eighth consecutive month
UK house prices registered a 1.3% fall in September, according to the Halifax.
The lender said the drop meant the annual fall now stood at 12.4%, with the cost of the average home in the UK now at £172,108.
It joined the Nationwide in claiming that the rate of decline was starting to stabilise when looking at three-month comparison figures.
But it said the state of the market would remain "challenging" as mortgage availability was still tight.
The annual rate is calculated using a comparison of the past three months compared with the same three months a year ago, aiming to cut out any short-term volatility.
When comparing prices in just September with the same month the previous year, the drop in prices reaches 13.3%, the biggest recorded by the Halifax.
September was the eighth consecutive month that prices fell compared with the previous month.
The average price of a UK home is close to that seen in January 2006.
"The ongoing pressures on householders' income, combined with the reduction in the availability of mortgage finance mean that market conditions will remain challenging," said Martin Ellis, chief economist at the Halifax.
But he welcomed the move by the Bank of England's Monetary Policy Committee to cut interest rates by half a percentage point to 4.5% on Wednesday.
"Lower interest rates will help mortgage borrowers faced with increasing pressures on their finances and provide a valuable support to the housing market," Mr Ellis said.
Prices declined by 5.2% in the third quarter of the year, close to the 5.1% fall of the previous three months. This was evidence that the pace of decline was stabilising, Mr Ellis said.
But with food and fuel prices having risen over the last year, and wages failing to keep up with the increase, households had less discretionary income.
"The resulting pinch on incomes, combined with the high level of average house prices in relation to earnings, has made it difficult for potential house purchasers to enter the market," he said.
Others agreed that the pace of decline could stabilise soon.
The year-on-year falls in house prices should hit a maximum of 15% next month and fall no further, according to Ray Boulger, of mortgage brokers John Charcol.
Prices were still rising up to October last year, before the effect of the credit crunch hit. As a result the year-on-year comparisons have been striking in recent months, he said. He said the Halifax figures were "not surprising".
But Howard Archer, chief UK and European economist at Global Insight, said he expected house price falls to continue.
"Faster rising unemployment, heightened concerns over the economic outlook and widespread expectations that house prices will continue to fall markedly seem set to depress housing market activity and prices for some considerable time to come," he said.
Despite hopes that Wednesday's rate cut will spur lending and boost the housing market, banks have been slow to pass on previous rate cuts to new and existing borrowers, as they continue to scale back lending.
The latest Bank of England figures show the average mortgage rate paid by new borrowers rose from 5.88% in August 2007 to 6.1% in August 2008 despite a three-quarters of a percentage drop in the Bank rate over the same period.
The average mortgage rate for those with existing mortgages has dropped from 5.91% in August 2007 to 5.83% to August 2008, although it has fluctuated during the year.
These cuts made by the Bank of England's Monetary Policy Committee have benefited existing borrowers, mainly those on tracker rates.
Earlier this month, the Royal Institution of Chartered Surveyors reported that completed property sales in August were 47% lower than in the same month a year ago.