Meanwhile, Hometrack this morning reported that house price rises are stagnating.
It said that while house price growth has continued this month, it is at half the rate three months ago.
Average prices rose by just 0.3% in June, while there was no rise at all in demand, measured by the number of new applicants.
Although time on the market has gone down, to 5.9 weeks, the percentage of asking price being achieved has slipped to 96.6% – lower than the last four months.
Hometrack said that it is a sign that agents are finding it harder to sustain price rises.
Richard Donnell, director of research at Hometrack, said: “Pent-up demand has been feeding into the market over the last 18 months, creating upward pressure on house prices.
“This trend now appears to be running out of steam, with no change in demand over the month.”
Hometrack now expects the rate of house price growth to slow down further – partly due to the Mortgage Market Review (MMR), and partly due to talk of interest rate rises.
Separately, Rightmove said that most people are paying under the asking price, despite talk of an over-heated market – and despite sellers jacking up their prices by nearly 8% in the last year.
Rightmove said it believes most buyers will continue to negotiate under the asking price, because of the MMR making it more difficult to get loans.
However, unlike Hometrack, Rightmove did say that the gap between asking price and selling price is narrowing.
The portal made its remarks after the NAEA claimed that in May, 19% of properties were sold at over the asking price.
The NAEA said that buyers who could not increase their offers risked being priced out of the market – although it did add the warning that the MMR could slow down sales.
But Rightmove has made it clear that its own findings and figures look as though the market in general is a very long way from over-heating.
It said that 72% of buyers in England and Wales paid under the asking price in the past 12 months. Even in London, 53% of buyers paid less.
Nationally, says Rightmove one in five (21%) paid exactly the asking price and 7% paid over.
The portal has based its figures on a poll of over 6,000 people who bought a property in the last year.
Miles Shipside, Rightmove director, said: “Talk of a national housing bubble is unfounded.
“Even in London, over half of buyers paid under the asking price.
“Although people are putting in offers under asking price and are still doing so in the current market, from our data we know that the discount from asking to sold price has narrowed.
“In 2012 properties achieved around 95% of the asking price, and in 2013 this average figure increased to around 97%.
“The Mortgage Market Review’s more stringent criteria makes it likely that people will continue to offer less than the asking price, especially if the new rules mean they are offered a lower mortgage than they were expecting.”
In a third report, there were 41,757 mortgages lent last month for house purchase by the big high street banks.
While this was steady compared with April, it was down from the 48,412 approvals in January.
The figures are reported by the British Bankers Association.