UK house prices dipped by 0.2% in June, according to the Nationwide, while annual price growth fell to 4.1% - the lowest level since July 1996.
A rate cut would encourage more deals, Nationwide says
Prices in the three months to June were up 0.8% against the previous quarter, the building society added.
"While the weather was hotting up, house prices in June cooled," the Nationwide said, adding price growth this year had been "almost horizontal".
The survey said the price of an average house in June was £157,791.
Nationwide said that activity levels in the market had "stagnated" recently, after a pick-up in the first few months of the year.
It noted that estate agents reported a continued stand-off between buyers and sellers, with vendors under no economic pressure to cut prices.
Affordability is "deteriorating", the society said, but if interest rates are cut in the autumn "this will improve and may mean that only small price adjustments will be necessary to bring some liquidity back to the market".
The Bank of England's monetary policy committee (MPC) meets next week to discuss interest rates, and, since the release of the last meeting's minutes, speculation has risen that a rate cut could be seen in the next few months.
"The dilemma the MPC faces is that if it reduces rates now, it could encourage further borrowing, which is precisely the reason why it felt the need to increase rates last year," said Nationwide group economist Fionnuala Earley.
"But if it doesn't, it risks a more protracted slowdown and all that brings with it."
Looking at the April-to-June quarter, Scotland and Northern Ireland were the only areas in the UK where annual house price growth remained in double figures, the Nationwide said.
However, in the first quarter, eight of the 13 regions covered by the Nationwide had seen price growth rates above 10%.
Other recent house price surveys have also indicated that the property market has slowed sharply in 2005.
Last month's survey from the Halifax said the market had been "flat", with prices having fallen 0.1% since the start of the year.
However, there have also been some signs that the market is beginning to level off.
On Wednesday, figures from the Bank of England showed the number of house purchase approvals hitting a 10-month high of 96,000 in May, raising hopes that the market is stabilising.
Also the last survey from the Royal Institution of Chartered Surveyors (Rics), despite reporting a fall in prices, found that its members were anticipating a pick-up in the market later this year given that interest rates appear to have peaked.