* UK industrial output and construction disappoint forecasts
* NIESR estimates UK economy grew 0.2 pct in 3 months to May
* Little sign weaker currency is boosting export volumes
* Analysts say renewed QE possible if growth falters (Adds NIESR estimate of growth, AXA comment)
LONDON, June 9 (Reuters) - Britain's economy appeared to be struggling to pick up pace even before Friday's inconclusive election result, with industrial output rising less than expected in April after a poor start to 2017.
The combination of a lack of economic momentum and the heightened uncertainty about how Prime Minister Theresa May can advance her plans for Brexit might prompt her new government to relax its grip on spending, some analysts said.
Industrial output rose 0.2 percent on the month in April after falling for three months. It was much weaker than a forecast 0.8 percent, and over a three-month period it contracted for the first time since November, the Office for National Statistics said on Friday.
Manufacturing, which is part of overall industrial output, also saw output rise 0.2 percent in April, compared with a forecast of 0.9 percent in the Reuters poll.
The construction sector was much weaker than expected too.
After last year's shock decision by voters to pull Britain out of the European Union, Britain is now facing more political upheaval after May's unexpected failure to win a parliamentary majority.
"There is clearly a risk that today's election result causes growth to weaken towards the end of the second quarter," Ruth Gregory, an economist with Capital Economics, said. "That said, this is unlikely to spell disaster since the economy has proved pretty resilient to political uncertainty in the recent past."
Britain's economy slowed sharply in the first three months of 2017, making it the worst performer among the Group of Seven nations after outpacing its peers in 2016, despite the shock of the Brexit vote.
As well as rising inflation and slow wage growth weighing on consumers, the economy now has to contend with heightened political uncertainty about Britain's ability to proceed with its plan to leave the European Union.
Britain's economy grew by a below-par 0.2 percent in the three months to May, the National Institute of Economic and Social Research, a think tank, said on Friday.
"The subdued performance in the economy throws the political turmoil of a hung parliament into sharp relief," NIESR director Jagjit Chadha said. "People are looking for answers to low levels of economic growth, limited improvements in productivity and falling real wages."
BOE BACK IN ACTION?
Investors are watching closely to see if May responds to the increase in support for the opposition Labour Party by relaxing her grip on public spending, something which would boost the economy.
Chris Iggo, fixed income chief investment officer at AXA Investment Managers, said that if the government failed to boost the economy, the Bank of England might resort to reviving its massive bond-buying programme again.
The BoE said before the election that it expected some of the impact of slower consumer spending would be eased by stronger exports driven by the pound's fall since the Brexit vote last year.
ONS data showed on Friday that Britain's goods trade deficit narrowed by more than expected to 10.4 billion pounds ($13.2 billion) in April.
But the smaller deficit was due to a sharp fall in goods imports with volumes in monthly terms down more than 5 percent in April, almost reversing a surge in March. Exports edged down.
Over the three months to April, goods exports rose 2.1 percent while imports were flat. But the ONS said there was no sign yet that exporters were taking advantage of sterling's weakness to cut their foreign-currency prices and strengthen their competitive advantage.
"Britain won't enjoy a trade boost until exporters reduce margins and seek greater market share instead," Samuel Tombs, an economist with Pantheon Macroeconomics, said.
The ONS said construction output in April fell by 1.6 percent from March and was down 0.6 percent on the year. The Reuters poll had pointed to growth of 0.3 percent on the month but a fall of 0.4 percent compared with April last year. ($1 = 0.7853 pounds) (Editing by Jeremy Gaunt)