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It said house prices rose 0.7% last month, up from 0.4% the month before and 0.2% in May. The latest rise took the annual rate of increase up to 11.2% from 10.7% in June.
But Halifax chief economist Martin Ellis said the fact that this was the fourth consecutive month in which prices had grown at less than 1% was proof of slowdown in response to five interest rate rises over the past year.
The Bank of England holds its latest meeting today but is not expected to put rates up this month.
"We expect the downward trend in house price growth to continue as the five interest rate rises since last summer have an increasing impact on household spending and housing demand.
"Sound economic fundamentals, high levels of employment and a shortage in the number of properties available for sale, particularly in London and the south east, will, however, continue to support house prices."
Mr Ellis added that the Halifax had recently changed its forecast of house price growth for 2007 as a whole to 6% from 4% but this was more due to stronger-than-expected rises in the first four months of the year rather than more recent increases.
The Halifax report contrasted with that of the Nationwide last week which suggested prices rose only 0.1% in July. But data from the Bank of England this.....continued below
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