Construction output growth of 1.8pc in December compared with November was also stronger than expected.
It came as separate data on Friday showed Britain's trade deficit narrowed to £8.6bn in the final three months of the year, down from £14.1bn in the third quarter, as exports rose.
While Kate Davies, a statistician at the ONS, said there was "little evidence" that the fall in the value of sterling after the Brexit vote had helped to reduce the trade balance, recent survey data suggest the weaker pound has helped to boost the UK's competitiveness.
Barclays said official production and services turnover data showed growth in the second half of 2016 was "driven primarily by export-led demand", with domestic growth "broadly flat" over the same period.
"Exporters appear to be in the driving seat," said analysts Andrzej Szczepaniak and Fabrice Montagne.
Martin Beck, an economist at Oxford Economics, said there were signs that growth was becoming a little less reliant on consumer spending.
"The week offered some glimmers that a rebalancing in economic activity away from consumption and towards production and exports may be in train," he said.
Barclays said there was a strong chance that official economic growth figures could be upgraded to 0.7pc for the final three months of the year, up from an initial estimate of 0.6pc.
This would represent the strongest quarterly growth in more than a year.
The National Institute of Economic and Social Research (Niesr) estimated on Friday that the quarterly pace of growth had picked up to 0.7pc in the three months to January amid "robust consumer spending" and a rise in production output.
Alan Clarke, an economist at Scotiabank, said growth for the final quarter of 2016 would be upgraded to 0.7pc provided that the services sector, which powers more than three quarters of UK output, rose by more than 0.15pc month-on-month in December.
"Our economic model has shown the loosest financial conditions for decades - this is clearly supporting activity," he said.
Scott Bowman, an economist at Capital Economics, said stronger export growth suggested net trade boosted growth in the final quarter, after subtracting an average of 0.6 percentage points in the first three quarters of the year.
- The Telegraph UK