One swallow doesn’t make a summer, but how about two? After the Nationwide reported a 1.2% rise in house prices in May, the Halifax went one better, saying they rose by 2.6%. The two measures differ on the year-on-year fall, the Nationwide’s 11.3% contrasting with the Halifax’s 16.3%, but they are telling a similar story. Are house prices bouncing back as quickly as they fell?

I don’t think so, and it would not be good news if they did. The housing market is slowly coming back to life after having its lifeblood, mortgage availability, cut off. The last thing we need is for prices to start surging again and it is unlikely that they will. Both Halifax and Nationwide attached health warnings to their numbers.

Nonetheless, a consistent story is now emerging in the housing market. Activity is slowly recovering and the fall in house prices is beginning to level off. A semblance of normality returning.

What is that normality? The Bank of England last week produced figures showing that new mortgage approvals rose to 43,201 in April, the third successive monthly rise, and an increase of 57% from the low point reached in November last year.

Simon Rubinsohn of the Royal Institution of Chartered Surveyors thinks monthly approvals will rise to between 60,000 and 65,000 by the end of the year. Would a recovery to these levels stabilise prices? Probably. The conventional wisdom is that between 70,000 and 80,000 approvals are needed to put a floor under the market, but that reflects pre-crunch levels of activity. If housing supply continues to be limited, around 60,000 monthly approvals should be consistent with price stability.

The Halifax and Nationwide’s price jumps suggested that price action is returning even before we have reached these levels, though both say it is too early to call the turn. The Land Registry said prices slipped by 0.3% in April, after a 0.4% fall in March. It thinks we are moving into a period of more modest monthly falls.

Not everything is entirely logical in the housing market but that tells us a fairly logical story. On one side activity is gradually picking up. On the other, the pace of house price falls has slowed. At some stage, probably over the next few months, the two will meet in the middle and the market will have reached an equilibrium. Barring accidents.

- Falling house prices are not just a British phenomenon; in the year to the end of March 2009, they went down in 26 of the other 31 countries surveyed by the Global Property Guide. Latvia, where the economy is in freefall, recorded the poorest performance, with prices down by 45.8%; in Dubai, they dropped by 34%. Israel and Thailand bucked the trend, with prices up by 6.36% and 4.63% respectively. Other risers included Switzerland, up 4.3%. Its market was buoyed by a surge in the number of foreign residents.