* Annual rate of decline slowest since August 2008
* Lack of supply drives improvement but may be temporary
By Christina Fincher
LONDON, May 29 (Reuters) - British house prices rose for the second time in three months in May, slowing the annual rate of decline to its weakest since last August, the Nationwide building society said on Friday.
Nationwide said the average house price rose 1.2 percent during May, the second rise since March when house prices turned higher for the first time since October 2007. The annual rate of decline slowed from 15 percent to a nine-month low of 11 percent.
The mortgage lender attributed the improvement to the lack of new properties coming onto the market but cautioned that rising unemployment and restricted lending meant prices were likely to resume their downward path.
Martin Gahbauer, Nationwide's chief economist, noted that during the downturn of the early 1990s there were many months when prices rose, only to fall again.
"Although the short-term trend in house prices has clearly improved from where it was at the beginning of the year, it is still too early to say that the market is turning definitively," he said.
"In the current downturn, the combination of rapidly rising unemployment and tight access to credit implies that the last of the price declines has probably not been seen yet."
The figures chime with other surveys in suggesting record-low interest rates have fuelled a rise in new buyer inquiries. However, mortgage lenders are still reluctant to lend to those without a significant equity cushion and figures from the Bank of England showed the country's top six banking groups scaled back lending to home owners last month.
The lack of supply may also be due to a change in legislation that requires home sellers to obtain more information before they can market their property.
Since April 6, vendors have been required to complete a "home information pack" before they can put their property on the market. Previously, they could market their home as long as they had applied for this information.
While there is growing optimism that Britain's economy may have passed through the deepest point of the recession, job losses are expected to climb for the rest of the year and most economists expect a recovery, when it comes, to be muted.
In the 1990s, house prices remained under downward pressure for several years after the recession had ended.
(Reporting by Christina Fincher; editing by Stephen Nisbet)