(Corrects headline, lead and third paragraph to show biggest calendar-quarter rise in factory output since Q2 2010, not Q3 1999, after ONS error)
* UK factory output rises by 1.4 percent in Q1 2014
* Construction growth revised up to 0.6 pct qq
* ONS says no material impact on earlier Q1 GDP estimate
* Trade deficit narrows more than expected
LONDON, May 9 (Reuters) - British factory output grew at its fastest pace in nearly four years during the first quarter of 2014 and the trade deficit narrowed, official data showed on Friday, adding to signs that the economy is rebalancing.
The Office for National Statistics said manufacturing output grew by 1.4 percent in the first three months of the year, up from 0.6 percent in the last three months of 2013.
This was the best calendar quarter since the second quarter of 2010, as the sector recovers from a steep slump after the financial crisis, and the strongest growth for any three month period since October 2010.
Britain's trade deficit in goods with the rest of the world also narrowed more than expected, sinking to 8.478 billion pounds ($14.37 billion), its lowest since December.
"UK trade and manufacturing numbers offer more support to those looking for earlier Bank of England rate hikes and stronger sterling," said James Knightley, economist at ING.
"All in all these reports are consistent with the UK economy gaining momentum," he added.
Earlier on Friday NIESR, one of Britain's leading economics research think tanks, revised up its expectation of economic growth for 2014 to 2.9 percent from 2.5 percent.
There was little immediate move in sterling or British government bond prices, as monthly changes in factory and industrial output growth were only a shade better than forecast.
Industrial output dropped 0.1 percent on the month in March after a 0.8 percent rise in February, while factory output grew by 0.5 percent, building on February's 1 percent rise.
Markets currently expect the Bank of England to raise interest rates from their record low 0.5 percent in the first three months of next year.
Britain's central bank has said it wants to see spare capacity mostly used up before it raises interest rates, and to see the recovery led less by household demand and more by stronger exports and business investment.
FACTORIES CATCH UP
Despite the recent pick up, manufacturing has lagged behind other sectors since the financial crisis, and is still 7.6 percent below its level in the first quarter of 2008, when overall economic output peaked.
The growth in factory output in the first quarter of 2014 was faster than the 1.3 percent pencilled into an initial estimate of gross domestic product released last month, but a steep fall in electricity and gas supply dragged down the broader industrial output measure.
Industrial output overall expanded by 0.7 percent in the first three months of 2014, up from 0.5 percent in the last three months of 2013 but slower than the 0.8 percent estimate in last month's GDP data.
Britain's economy overall expanded by 0.8 percent in the first quarter of GDP, and the ONS said that this estimate was not materially affected by Friday's new data on industrial output and construction output.
Construction grew by 0.6 percent in the first quarter of 2014, twice as fast as assumed in the GDP estimate, and in March was 6.4 percent higher on a year earlier - its strongest annual rise in six months and one driven by private housing.
But like manufacturing, construction is recovering from a low base and output is still more than 12 percent below its pre-crisis peak. By contrast, overall GDP is forecast to return to pre-crisis levels in the current quarter.
Last year the government launched Help to Buy, a scheme aimed at boosting demand for newly-built homes that has since been expanded to widen access to high loan-to-value mortgages.
House prices have risen by around 10 percent over the past year and are close to their peak before the financial crisis, fuelling concern that supply is not keeping up with demand and that parts of Britain are at risk of a property price bubble. ($1 = 0.5899 British Pounds) (Editing by Jeremy Gaunt)