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* UK house prices set fastest annual pace in nearly 7 years
* UK construction slows again in May, bottlenecks identified
* Too early to say if market at turning point- Nationwide (Updates throughout)
By Ana Nicolaci da Costa
LONDON, June 3 (Reuters) - Britain's house prices rose at their fastest annual pace in nearly seven years last month and signs of bottlenecks in the construction sector underscored the upward pressures on the market, surveys showed on Tuesday.
House price growth picked up to an annual pace of 11.1 percent in May, mortgage lender Nationwide said, fanning concerns that the property market could be overheating.
A separate industry survey showed the construction sector cooled a bit in May from a six-and-a-half-year high in January.
But supply shortages and wage growth at a 17-year high raised questions about how long the sector could keep up its strong growth.
"With supply constraints still persisting, there are some concerns about how this prolonged period of growth can be sustained over the course of 2014," said David Noble, chief executive at the Chartered Institute of Purchasing & Supply.
British house prices started to rise strongly last year, helped by record low interest rates and a recovering economy.
But a lack of new home-building prompted Bank of England Governor Mark Carney to single out the housing market as the biggest threat to Britain's economic recovery last month.
The European Commission on Monday also warned of risks, saying the British government should consider scaling back its Help to Buy mortgage guarantee scheme.
Tuesday's data showed house price growth slowing on a monthly and three-month basis, but analysts said it was too early to say whether the market was at a turning point.
"We have definitely seen a bit of a cooling in recent months," Nationwide chief economist Robert Gardner said.
"It will probably take us until the back end of the summer until we are sure what is really going on in terms of the underlying pace of growth."
Part of the problem is analysts do not know whether the recent slowing mortgage approvals has been due to new controls on lenders or whether lofty prices are putting buyers off.
New rules requiring lenders to make more stringent checks on the ability of borrowers to repay loans took effect in April.
Analysts expect the BoE to introduce new mortgage controls when its Financial Policy Committee meets on June 17 and to make those public when it publishes its financial stability report on June 26.
Options include making banks hold more capital against certain types of home loans or urging caps on how large a mortgage can be relative to a borrower's income.
Another possibility would be for the FPC to call on the government to lower the ceiling for properties qualifying for its "Help to Buy" mortgage guarantee plan. (Editing by William Schomberg/Ruth Pitchford)