UK house prices were unchanged in April and, overall, there has been no movement since January, according to the latest survey from the Halifax.
Activity may be picking up but prices aren't moving
Annual price inflation fell to 7.8% in April - the lowest level since June 2001 - from 9.7% in March.
"The annual rate is expected to continue to fall over the coming months," the Halifax said.
However, the bank noted there was evidence of a pick up in activity in the market after a slowdown last year.
The evidence included recent figures from the Bank of England which showed the number of mortgage approvals increased in March for the second month in a row.
Also, the Royal Institution of Chartered Surveyors reported a firming in housing activity during the first three months of the year.
"Overall there has been no movement in prices at the national level since January," said Halifax chief economist Martin Ellis.
But he added: "We appear to be entering a period of broad stability, particularly in terms of market activity.
"Sound fundamentals, particularly in the shape of the ongoing strength of the labour market and the low level of interest rates, should continue to underpin the market."
The Halifax's survey comes a week after the Nationwide building society reported a 0.9% rise in house prices during April.
However, the Nationwide also recorded a fall in the annual rate of property price inflation - to 7% from 7.9% - and noted that the overall trend remained "broadly flat".
Economic forecast group Capital Economics, which has predicted that house prices could fall, reiterated that the market had reached an "impasse", with buyers and sellers unable to agree on prices.
"We expect the pace of the slowdown to pick up as the year progresses, in line with more gloomy reports from surveyors and housebuilders," Capital Economics said.
Recent official figures have suggested some UK homeowners are struggling to cope, following five interest rate increases since late 2003.
According to the Department for Constitutional Affairs, the first three months of 2005 saw a 25% rise in the number of property repossession orders, against the same period in 2004.
Recent surveys from both the Halifax and Nationwide have indicated that the once-booming UK property market is now cooling.
The Halifax said that the slowdown could be good news for long-suffering first-time buyers, many of whom have been priced out of the market.
The bank said that the latest data showed the house price to earnings ratio had dropped from a peak of 5.63 in September 2004 to 5.48 in February.
"The easing in the house prices to earnings ratio over the past few months is expected to be sustained as earnings rise more quickly than house prices," said Mr Ellis.
"This will improve affordability for first-time buyers, enabling more to get a foot on the housing ladder."
Analysts noted that the price slowdown also makes a further rise in UK interest rates less likely. The Bank of England's Monetary Policy Committee (MPC) is to announce its decision on rates on Monday.
"The survey points to a further cooling of the UK housing market. As such, it provides marginal support for the MPC maintaining rates at current levels," said Richard McGuire at RBC Capital Markets.