The Office for National Statistics (ONS) said industrial production grew 0.5% between the third and fourth quarters of last year with manufacturing a major contributor with a 0.7% rise.
However that sector was up only 0.3% between November and December, slightly below expectations.
It means the sector shrank by 0.6% over the course of 2013, less than it did the year before but still the second annual drop in succession as its performance remains well below its pre-recession peak. December's improvement in trade was bolstered by rising oil, chemicals and aircraft exports and a fall in imports of aircraft and ships.
Chris Williamson, chief economist at Markit, said: "Part of the weaker result for the fourth quarter reflects the poor performance of the oil and gas sector, linked to temporary disruptions as well as the long-term trend of dwindling oil and gas reserves in the North Sea.
"The mining and quarrying sector, under which these activities fall, saw output drop by 1.09% in the fourth quarter."
Separately the ONS said the trade deficit fell from £3.6 billion in November to £1bn in December, the lowest monthly figure since July 2012 and the steepest month-on-month drop since records began in 1998.
The goods' deficit fell from £9.8bn to £7.7bn, while the surplus in services increased from £6.2bn to £6.7bn.
The ONS said the goods deficit with countries outside the EU had narrowed in each of the last six months. The trade deficit for the whole of 2013 was £29.9bn, an 11% fall on 2012.
Howard Archer, from IHS Global Insight, said: "There are signs in the December trade data that gradually improving domestic demand in the Eurozone and firming global growth is starting to feed through to help UK exports. Exports of traded goods to the Eurozone rose 2.8% in December while exports to non-EU countries were up by 1.2%.
"It is still hard seeing net trade making significant positive contribution to UK growth anytime soon, as imports are likely to continue to be underpinned by decent UK domestic demand."