"The mortgage market is expected to continue to face some ' significant opposition", which is expected to keep a constraint on demand.
Prices increased by 1.2% House in June, figures from Halifax show, but fell by 3.5% in the last 12 months.
End of June, the average price of a house in the UK was £ 163,049.
Last month improvement meant that the decrease in prices in the last three months reduced only 0.5% - for a year the smallest quarterly fall.
Low interest rates, an increase in the number of persons in employment and some tightening market conditions are expected to have been the main reasons for the improvement of recent price trends.
Typical mortgage payments for new borrowers have fallen from a peak of 48% of the average disposable income mid-2007 to 28% in the second quarter of this year.
It means that affordability on better than the average in the last 25 years proved to be an important factor in supporting the demand.
Housing Economist Martin Ellis has warned however that the market faces many obstacles.
"The market is confronted are expected to remain significant headwinds, demand to restrict the expected housing", he said.
"Low earnings, higher taxes and relatively high inflation further all pressure on household finances."
Figures show that although the market subdued, activity remain at least stable.
The number of mortgage approvals has remained within the range of 45,000 to 50,000 per month since early 2010.
And is encouraging, that approvals were in the three months from March to may of this year show 2% higher than in the last three months of Bank of England figures.
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