Rightmove says the property market slowdown has begun with the first fall in house prices this year in the first week of June.
Although overall asking prices increased by 2.6 per cent in May from the April figures, this includes a fall of 0.4 per cent in the first week in June.
The number of properties up for sale rose by 10 per cent, easing the supply shortages which have contributed to sharply rising prices.
Rightmove commercial director Miles Shipside says the figures could indicate the beginning of a sustained slowdown but he thinks the cooling of the market will be steady and gradual rather than sudden and dramatic.
Although generally more upbeat, Nationwide warns that there is a growing potential for a drawn-out period of low activity and low price growth.
The group's monthly house price index shows prices went up by 1.9 per cent in May, pushing the annual rise to 19.5 per cent. However, its house price forecast for the 12 months to December 2004 implies an average monthly rise of just 0.7 per cent for the remainder of the year.
Nationwide group economist Alex Bannister expects the combination of muted post-tax earnings' growth, further interest rate rises and a downgrading of homeowners' price rise expectations to slow the market.
He says: “In the absence of a recession and large increases in unemployment, significant downward pressure on prices would be unlikely.”
The most positive figures come from Halifax which says house prices rose by 2.2 per cent in May due to strong housing demand and supply shortages.
Chief economist Martin Ellis says the market has remained strong in Northern England and Wales and house price inflation in the South has picked up. He expects higher interest rates and increasing difficulties facing first time buyers to exert downward pressure on house price inflation later in the year and into 2005.
The number of first-time buyers as a percentage of all homebuyers dropped to 28 per cent after rises in February and March and is well below the historical average of nearly 50 per cent.
Hometrack records just a 0.6 per cent increase in average national house prices but its economists are the most positive about the future.
The firm's national demand index shows that while the number of properties for sale and the number of buyers registered rose in May, there continued to be significant excess demand which implies that further house price rises are expected in the coming months.
Hometrack housing economist John Wriglesworth says there are no signs of a slowdown and he does not expect significant interest rate rises this year.
He says: “The only economic factors that could precipitate a housing market crash are a doubling of interest rates, stamp duty or unemployment. None of these is expected by any UK economists either this year or next.”