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It marks the fifth consecutive period of GDP growth – the longest positive run since the financial crisis.
The Office for National Statistics (ONS) also said the economy is still 0.6% smaller than its 2008 peak.
Chancellor George Osborne said Tuesday’s figure showed that “Britain is coming back”, but that the recovery could not be taken for granted.
“The impact of the Great Recession is still being felt, but the foundations for a broad based recovery are now in place,” he added.
Chief economics correspondent, BBC News
Talk of quarterly growth accelerating to 1% in the first quarter of this year proved unfounded.
But with services, manufacturing and construction all registering expansion between January and March, a more balanced recovery seems to be developing.
Surprisingly, while the building industry may have been affected by the weather, the floods and storms of January and February do not seem to have had much of an impact on overall economic activity.
But while economies like the US and Germany have now moved ahead of their pre-recession peaks, the UK is still lagging a little behind.
It seems likely the economy will reach that milestone in the middle of the year.
“The biggest risk to economic security would be abandoning the plan that is laying those foundations.”
Tuesday’s growth figure – the ONS’s first estimate for the quarter – is a slight increase on the 0.7% recorded for the final quarter of 2013, and a rise of 3.1% on the same period a year ago.
But many had been expecting the latest figure to be even higher, at 0.9%.
UK manufacturing output grew by 1.3%, the ONS said, its strongest quarter for nearly four years.
And the service sector, which includes everything from hotels and leisure to accountants, grew by 0.9%.
Construction output, which grew by 0.3%, was affected by the storms and high rainfall in January and February, the ONS said.
But it added that the bad weather did not have a significant impact on overall GDP growth.
Agriculture was the only one of the four main industrial sectors to register a fall in output, dropping by 0.7%.
Source: BBC News