Construction output rose by 0.9% in the fourth quarter, the Office for National Statistics (ONS) said.
February construction output in the euro zone fell on the month, a fourth straight decline.
Also Tuesday, Euro zone construction output fell sharply in January, to its lowest level since 1997.
The ONS said output in the construction sector was higher than it had previously estimated.
In the first five months of the year, industrial construction output expanded at rates above 4 percent.
Do we really believe that the level of construction output was lower in January than in December?
Output in the construction industry grew by more than initially thought in the last three months of 2012.
And we know that the public sector accounted for around a third of total construction output in 2011.
The ONS report on output in the construction industry showed a 9.8% drop compared with November 2011.
Today's figures show construction output down by 5.2% in the second quarter, and nearly 10% smaller than a year ago.
Construction output dropped 4.8 percent from a year earlier, the agency said, not 3 percent, as it had estimated earlier.
Big falls in construction output were a factor when the UK was last in recession in the first half of 2012.
The ONS measures construction output from the activity of business in Britain, not including Northern Ireland, which conducts its own equivalent survey.
The estimate for construction output is based on published data for the first two months of the quarter, and an estimation for the third month.
There was fresh, weak data coming out of the European Union, as construction output declined by 0.4% in November, for an annual drop of 4.7%.
The ONS had already said that output from the construction sector fell by 3.9% between April and June compared with the previous quarter, compared with an earlier forecast of a 5.2% drop.
The Scottish Building Federation (SBF) said despite a "modest" rise in construction output during the last three months of last year, annual output from the industry remained at its lowest level for 10 years.
Stronger rises in factory output and the construction sector, together with continued falls in unemployment, could mean national income as measured by gross domestic product (GDP) is not shrinking as quickly as first estimated.
The index has been developed using data from existing quarterly indices of output from the production, services and construction sectors combined with agricultural output data and employee jobs data for the public sector.
The weakness in overall output reflected falls in construction, which is "unlikely to be repeated in 2013".
It is quite possible that the economy is stronger than the official statistics suggest: in fact, we already know that construction and industrial output were stronger in June than the ONS expected when they came up with their first estimate for the change in GDP in the second quarter.
The construction industry is continuing to contract with output down by nearly 5% quarter-on-quarter and down 7.5% year-on-year.
Output should pick up elsewhere in the economy including commercial construction, investment and inventories.
The Item Club highlights the importance of the large and diverse business services sector in being the main engine of growth, while manufacturing has stagnated and construction remains about 10% below its pre-downturn output.
Output of goods includes such branches as industry, agriculture, forestry, construction, other goods-producing branches.
The existing output supplies not only Nike but insulation used in Chinese refrigerators and in building construction.
Regular readers will be thrilled that our old friend, the construction sector, is in the frame again - the sharp fall in output in this sector in December is very much an estimate, which some consider a little fishy.
Distrust of the GDP numbers has prompted Capital Economics, a research firm based in London, to create its own proxy of economic activity, which includes electricity output, domestic freight volumes, cargo traffic at ports, passenger transport and floor area under construction.
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