CORRECTED (OFFICIAL)-UPDATE 1-UK industrial output suffers biggest drop since 2012 in December

(Corrects record in 9th paragraph provided by ONS on consecutive monthly declines to read 2012, not 2009)

* Steepest drop in industrial output since Sept. 2012

* Warm weather curbs demand for electricity

* Manufacturing slips for third straight month

By Andy Bruce and Ana Nicolaci da Costa

LONDON, Feb 10 (Reuters) - British industrial output suffered its sharpest monthly drop in December since 2012 as warmer than usual weather curbed demand for electricity and gas and manufacturing continued its decline, denting hopes for improvement this year.

Britain has been one of the fastest-growing major advanced economies in the world for the last couple of years. But it has relied heavily on domestically focused services for growth, frustrating plans for a better-balanced recovery.

Industrial output fell 1.1 percent month-on-month in December after a 0.8 percent drop in November, the Office for National Statistics said, worse than all forecasts in a Reuters poll of economists that forecast a 0.1 percent dip.

The figures add to a run of poor industrial output data from countries around Europe, including France and Germany, and is unlikely to allay worries about the global economy's health.

"December's sharp drop in industrial production will fuel concerns about the UK economic outlook as well as the unbalanced nature of growth," IHS Global Insight economist Howard Archer said.

The ONS revised down its estimate for industrial output in the fourth quarter to show a 0.5 percent drop from a 0.2 percent decline previously, reflecting a sizeable fall in electricity generation caused in part by unusually mild weather.

Britain's economy expanded 0.5 percent in the fourth quarter, but this early estimate could easily be trimmed if poor construction output numbers on Friday follow the industrial data, Pantheon Macroeconomics economist Samuel Tombs said.

The manufacturing sector failed to contribute to British economic growth in 2015 and the latest figures do not augur well for this year.

Output in manufacturing fell for a third month in a row for the first time since early 2012, dropping 0.2 percent on the month after falling 0.3 percent in November. Economists had expected output to edge up 0.1 percent in November.

A separate survey from the Bank of England's regional agents also showed a slowdown in manufacturing, with exports suffering from the global economic slowdown.

Both industrial and manufacturing output saw their biggest annual declines in December since mid-2013, the data showed.

Finance minister George Osborne has warned the economy is facing a "dangerous cocktail" of risks from overseas in 2016, as growth slows in major emerging markets, stock markets tumble and a slump in oil prices reduces demand from oil-exporting nations.

Output from the oil and gas extraction sector fell 4.6 percent on the month, the biggest decline since September.

Brent crude oil prices slid 16 percent in December and 35 percent for 2015 as a whole. (Editing by Catherine Evans)