* Houses prices fall 0.6 pct in June vs May -Halifax
* But annual pace of house prices growth rises again
* Economists say momentum may be near peak (Recasts, adds economist reaction and context)
By Andy Bruce
LONDON, July 9 (Reuters) - Britain's housing market lost a little steam in June as prices dipped from the previous month, although faster annual growth suggested the rapid market upturn still has momentum, a survey from mortgage lender Halifax showed.
House prices dipped 0.6 percent in June from May when they leapt 4.0 percent, their fastest monthly pace in more than 11 years. Economists polled by Reuters had expected house prices to rise 0.2 percent in June.
Bank of England Governor Mark Carney has cited the rapid run-up in house prices, notably in London, as the biggest domestic risk to financial stability.
House prices soared 8.8 percent year-on-year in the three months to June, the survey showed on Wednesday, the fastest annual growth since October 2007, and following a rise of 8.7 percent in the previous three-month period.
Economists were doubtful that pace can be sustained for long.
"The year-on-year (rate) is still rising but I suspect we're probably not far off the peak. There is evidence to suggest the housing market is generally cooling," said Peter Dixon, economist at Commerzbank.
A separate survey from lender Nationwide last week showed house prices rose at their fastest rate in over nine years, led by surging prices in London.
But mortgage approvals fell in May to their lowest level since June 2013.
Tighter mortgage affordability rules were introduced in April.
The Bank of England last month announced measures to curb rising debt and allow wages to catch up with house prices, the impact of which has yet to be seen.
The BoE said no more than 15 percent of mortgages offered by lenders can be for loans worth over 4.5 times a borrower's income, and it has asked banks to ensure borrowers can cope with bigger rises in interest rates than before.
Last week, the BoE's deputy governor for financial stability, Jon Cunliffe, said rapidly rising house prices are a problem that has spread beyond London.
Halifax said on Wednesday that the economic recovery would continue to support housing demand, along with rising employment and growing consumer confidence. But it pointed out that real earnings growth remains sluggish. (Editing by Susan Fenton)