* Sept house prices +0.9 pct m/m, unchanged y/y - Nationwide
* Sept construction PMI falls to 46.7 from 47.7 -CIPS/Markit
* Homeowners repay 7.0 bln stg of mortgage debt in Q2 - BoE
By David Milliken and Kylie MacLellan
LONDON, Oct 2 (Reuters) - British house prices rose to their highest level in a year in September and there was the first increase in house-building in nearly two years, but this was not enough to stop an overall decline in construction activity.
Moreover, economists warned that the recovery in house prices from February's near five-year low was slowing and Bank of England figures showed existing homeowners repaid mortgage debt at a near-record rate in the three months to June.
Building society Nationwide said house prices rose 0.9 percent in September, slightly better than economists' forecasts of 0.7 percent but less than August's 1.4 percent rise.
September's gain left prices unchanged on the year -- the first time since March 2008 that prices have not declined on a year-on-year basis. The average price of a British home is now 161,816 pounds ($257,900) -- 13 percent below the peak in October 2007 but 10 percent up on February's level.
Economists said support for the housing market was largely coming from a lack of supply of new properties and the greater affordability of those properties that are on the market.
"To the extent that downside risks have eased and confidence has improved it may be that prices are rising back to more appropriate levels ... while still down significantly from the peak," said Allan Monks, UK economist at JP Morgan.
"If these arguments are correct, the strength of the recent price gains is likely to loose some steam in due course," he said.
Nationwide economist Martin Gahbauer said high unemployment and restrictive credit conditions put a limit on how fast demand could increase, meaning it was unlikely house prices would continue to increase at the strong rate seen in recent months.
Economists also said higher prices would be likely to increase supply, tempting back sellers who had been put off by sharp price falls earlier in the year.
CONSTRUCTION WEAK
Construction activity slowed further in September, and at a faster pace than in August.
Purchasing managers' data from Markit and the Chartered Institute of Purchasing and Supply showed the headline PMI index fell to 46.7, its lowest level since June.
While the housing component showed its first growth for 22 months, rising to 50.3 from 48.2, the pace of contraction in commercial property and civil engineering accelerated.
"Though the industry is not contracting as quickly as it was earlier in the year, firms are struggling to adjust to comparatively low levels of activity, as reflected by employment levels which took another hefty hit and have dropped consecutively for 16 months," said CIPS chief executive David Noble.
Prospects for a consumer-led recovery also took a knock from Bank of England data which showed households paid down 7.0 billion pounds worth of mortgage debt between April and June -- only slightly less than the record 7.3 billion repaid in the first three months of the year.
This amounted to 2.9 percent of post-tax income.
"Housing equity withdrawal has been used significantly to support consumer spending in recent years. Consequently, the sharp turnaround from substantial withdrawals up to and including the first quarter of 2008 has added to the constraints on consumer spending," said IHS Global Insight's Howard Archer.
* For a graphic showing the Nationwide house price index and mortgage approvals, see: http://graphics.thomsonreuters.com/109/UK_MTGNWI1009.gif
(Editing by Mike Peacock)