The mortgage market is likely to continue to face some 'significant headwinds' which are expected to keep a constraint on demand.
House prices increased by 1.2% in June, figures from Halifax show, but have fallen by 3.5% over the past 12 months.
At the end of June, the average price of a home in the UK was £163,049.
Last month's improvement meant that the fall in prices over the last three months narrowed to just 0.5% - the smallest quarterly fall for a year.
Low interest rates, an increase in the number of people in employment and some tightening in market conditions are likely to have been the main factors behind the recent improvement in price trends.
Typical mortgage payments for a new borrower have fallen from a peak of 48% of average disposable income in mid-2007 to 28% in the second quarter of this year.
It means that affordability is at a better level than the average over the last 25 years and has proved an important factor in supporting demand.
However, housing economist Martin Ellis has warned that the market still faces many obstacles.
"The market is likely to continue to face significant headwinds which are expected to constrain housing demand," he said.
"Low earnings growth, higher taxes and relatively high inflation are all continuing to put pressure on household finances."
Figures show that while the market is subdued, activity levels are at least remaining stable.
The number of mortgage approvals has remained within the range of 45,000 to 50,000 per month since the beginning of 2010.
And, encouragingly, approvals in the three months from March to May this year were 2% higher than in the previous three months, Bank of England figures show.
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