UK annual house price growth lowest since mid-2013 - Nationwide

* UK house prices grow at slowest annual pace since June 2013

* Nationwide warns slowdown might not last

* GRAPHIC: Nationwide house prices http://r.reuters.com/jad24s (Adds detail, context)

By Andy Bruce

LONDON, Aug 27 (Reuters) - British house prices rose this month at the slowest annual pace in more than two years, according to mortgage lender Nationwide, although it warned the slowdown might not persist unless house-building picks up significantly.

House prices rose 3.2 percent year-on-year in August, the weakest annual rate since June 2013, compared with a 3.5 percent rise in July.

Economists polled by Reuters had expected the rate of growth would fall to 3.1 percent this month.

On a monthly basis, house prices rose 0.3 percent, in line with expectations and down slightly from a 0.4 percent increase in July.

Nationwide said the figures were further evidence that annual house price growth may be stabilising close to the pace of earnings growth, with regular pay excluding bonuses at just under 3 percent during the second quarter.

"However, survey evidence cautions that this trend may not be maintained unless construction activity accelerates," said Robert Gardner, chief economist at Nationwide.

"Surveyors reported the lowest ever number of properties on their books in July -- on data extending back to the late 1970s -- whilst new buyer enquiries picked up."

Gardner added that a significant increase in construction activity would be needed to avoid affordability becoming further stretched in the years ahead.

The government last month announced a plan to remove obstacles to building new houses after it helped cause a surge in house prices in 2013 by backing subsidies for people trying to get on the property ladder.

Data from rival mortgage lender Halifax has pointed to a stronger pace of annual house price growth, although it too has slowed recently.

But there have been signs activity is picking up, after the introduction of tougher rules on lending slowed the market through most of 2014.

The British Bankers' Association said mortgage approvals rose in July to their highest level since February 2014. Official figures from the Bank of England also show mortgage approvals have risen in most months this year.

BoE Deputy Governor Ben Broadbent said earlier this month he didn't view the housing market "with great alarm".

A Reuters poll of economists on Wednesday suggested house price growth is likely to slow next year. (Editing by Toby Chopra)