UK house prices rose by 1.2% in June, the smallest gain since November, according to the latest survey from the Halifax, the UK's biggest lender.
Halifax says housing demand is being curbed
It also reported that house prices were 21.5% higher in the past three months than in the same period in 2003.
The seasonally-adjusted index rose 2.2 % month-on-month in May, or 20.4% in the three months to May compared with a year earlier.
The average house price has now risen to £159,735, the survey found.
Earlier this week the Nationwide also said that house price growth had eased in June.
Their figures and those of the Halifax are often similar, as they are both based on the price agreed after a survey by their mortgage customers.
However, they are based only on property sales financed by mortgage lending, ignoring sales which are transacted on a cash basis.
Nationwide said it was sticking to its forecast for a 15% rise in house prices over the year.
A separate report by property website Hometrack, on Monday, showed average prices grew by 0.4% in June, compared with a 0.6% increase a month earlier.
According to the Halifax, house prices increased in all regions in the three months to June, with Scotland recording the biggest rise.
But Martin Ellis, Halifax chief economist, said: "House prices increased by 1.2% in June. This was the smallest gain since last November and was below the average 2.1% rise in the previous six months.
"This suggests that the recent increases in the cost of borrowing are beginning to curb housing demand."
The Halifax found that after Scotland, the next biggest gains were in the East Midlands (8.7%), North (7.8%) and North West (7.6%).
The smallest price rises in the second quarter were in Greater London (1.8%), Northern Ireland (1.8%) and the South East (3.2%).
Over the past year, the biggest price rises have been in northern England and Wales.
The North has put on 36%, Wales 36%, the North West 34%, and Yorkshire and Humberside 28%.
But the Halifax said that despite these strong performances, there were signs "of a slowdown in these areas", with prices rising by less in the past three months than in the preceding quarter.
However, Henk Potts, an analyst at Barclays Stockbrokers, said that despite the slowdown, he did not believe the housing market was heading for a crash.
"There are signs that it has been slowing down but interest rates are not the only thing that drive house prices," he said.