Halifax, Britain’s biggest mortgage lender, took the occasion of a 0.5 per cent fall in its measure of house prices to highlight evidence that the housing market is stabilising.

Last month’s dip contrasted with a rise of 2.6 per cent in May and a 0.9 per cent increase reported by Nationwide, whose index has risen three times in the past four months.

Martin Ellis, Halifax’s housing economist, pointed out that a 1.9 per cent fall in his index during the second quarter of this year was the smallest since the first three months of 2008.

It brings the year-on-year decline down to 15.0 per cent from 16.3 per cent in May and 17.7 per cent in both February and April.

“These figures provide evidence that the underlying pace of house price decline is easing,” Mr Ellis said.

He noted signs of a modest improvement in housing market activity and that the number of mortgages approved for house purchases in May was ten per cent higher than a year earlier.

Low interest rates and cheaper house prices have stimulated demand, he added, while relatively few homes are coming up for sale.

Mr Ellis concluded: “Whilst there have been encouraging recent signs of improvement, the outlook for the UK economy remains uncertain with unemployment set to continue rising for some time. Overall, we expect to see a continuing mixed pattern of monthly house price rises and falls over the remainder of 2009.”

Howard Archer, chief UK economist at IHS Global Insight, struck a cautious note, saying: “The Halifax data reinforce our doubts that house prices have bottomed out and we certainly do not think that we are at the start of a renewed sharp upward trend.

“Further relapses in house prices remain highly likely and they could yet fall by another ten per cent from current levels.

“Much will clearly depend on whether the economy can sustain its recent overall improvement, how much further unemployment rises and how many properties come on to the market over the coming months.”

Halifax put the average house price last month at £157,713, down from £158,541 in May and close to where it was in the spring of 2004.

This average house price is 4.33 times the annual average earnings of a full-time male employee, down from a multiple of 5.07 in June last year.

Halifax calculates that the average cost of owning a home has fallen by 17 per cent, or £1,468, over the 12 months to April, to £7,298. That is equivalent to 23 per cent of average UK full-time earnings, down from 28 per cent last year and less than at any time since 2006. The main factor in this decline has been the fall in mortgage interest rates.

Monthly mortgage repayments accounted for an estimated 21.6 per cent of average household income – before tax – last month for existing borrowers.

This was marginally above the long-term average of 20.4 per cent but still the lowest proportion of income devoted to mortgage payments since mid-2004 and down decisively from a peak of 26.9 per cent in October last year. Since then the average rate paid by existing borrowers has fallen to 3.59 per cent in May from 5.82 per cent.