* Goods trade deficit widens unexpectedly in June
* Exports weaken as sterling strengthens
* Construction output rebounds in June (Adds economist reaction, detail)
By Andy Bruce
LONDON, Aug 8 (Reuters) - Sagging exports pushed Britain's trade deficit to a five-month high in June, suggesting a more balanced economic recovery still looks a way off, although the construction industry recovered from a dip in May.
Exports of British goods to countries outside the European Union fell to their lowest level since September 2011, coinciding with the pound hitting a near six-year high against the dollar.
The country's total goods trade deficit grew to 9.4 billion pounds ($15.8 billion) in June, its highest level since January, from 9.2 billion pounds in May, official data showed on Friday. Economists had forecast a gap of 8.8 billion pounds.
The data dampened hopes that exports will soon make a greater contribution to Britain's consumption-led economic recovery, but separate construction data and a recruitment survey still pointed to strong domestic demand.
"The (trade) problem is largely out of the UK's hands," said Martin Beck, senior economic advisor to the EY ITEM Club, who pointed to weak growth in the euro zone - Britain's biggest export market.
"This is likely to remain the case for the foreseeable future. Sterling rose further in July while the euro zone economy looks set for little or no growth in Q2."
By contrast, Britain's economy grew 0.8 percent in the second quarter, according to an early estimate.
The Bank of England - which will release updated economic forecasts next Wednesday - expects that pace of growth to slow slightly later this year.
The pound hit an eight-week low against the dollar after Friday's data, pressured mostly by news that the United States had authorised air strikes against militants in Iraq.
Including Britain's surplus in trade in services, the overall trade deficit rose to 2.5 billion pounds from 2.4 billion pounds, also the biggest since January, the Office for National Statistics (ONS) said.
Exports of goods decreased in June by 0.4 billion pounds, reflecting falls in oil and manufactured goods. Imports also declined, but only by 0.1 billion pounds.
Construction data from ONS added to survey evidence that house building has surged recently, as its monthly measure of new housing hit its highest levels since the series began in 2010.
Overall construction output - which accounts for just over 6 percent of the British economy - rose by 1.2 percent in June after falling by the same percentage in May. Year-on-year growth rose to a three-month high of 5.3 percent from 3.9 percent in May.
Still, construction output is 10.3 percent below its level in the first quarter of 2008, before the financial crisis.
"We expect (the improvement) to continue, particularly as the housing market now seems to be shaking off the effects of tougher mortgage rules, with loan approvals rising 8 percent in June," said Rob Wood, economist at Berenberg.
A Markit purchasing managers' survey showed house building rose last month at the fastest rate since November 2003, although overall growth in construction cooled slightly.
The ONS revised up its earlier estimate of construction output in the second quarter to show no change, compared with a 0.5 percent decline previously.
The revision would have no impact on its 0.8 percent estimate of GDP growth during the same period, the ONS said.
A survey of recruitment companies on Friday also pointed to strong domestic demand, as British businesses stepped up hiring last month and continued to offer higher starting salaries. (Additional reporting by Costas Pitas; Editing by Susan Fenton)