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But the economy is still smaller than its peak before the 2008-09 recession, underscoring why the Bank of England has said it will not be raising interest rates quickly.
Output was 3.1% higher in the first quarter compared with the same period last year, the biggest rise since the late 2007, the Office for National Statistics said.
Gross domestic product rose by a quarterly 0.8%, picking up a bit from growth of 0.7% in the last three months of 2013, the ONS said.
"The UK economy is in the sweet spot of the economic cycle, with growth powering ahead of our major competitors and inflation falling away," Ian Stewart, chief economist at Deloitte, said.
Economists taking part in a Reuters poll had forecast quarter-on-quarter growth of 0.9% and 3.2% in yearly terms. Several forecasters had expected the quarterly growth rate to come in as high as 1%.
The pound weakened against the dollar and British government bond prices briefly rose after the data.
The acceleration will help Prime Minister David Cameron as he tries to convince voters that his Conservative Party should be returned to power in next year's elections to carry on restoring Britain to financial health.
"Today's figures show that Britain is coming back," finance minister George Osborne said in a statement. "But we can't take that for granted. We have to carry on working through our long-term economic plan."
Britain's economy was 0.6% smaller than at its peak in the first quarter of 2008 after the recession wiped 7.2% off total output, the ONS said.
But excluding the oil and gas sector, which is in decline, output was 0.3% higher than in early 2008.
Bank of England Governor Mark Carney was quoted as saying on Tuesday that the economic recovery is starting to broaden and there are early signs that it will be sustainable.
GROWTH IN ALL SECTORS
Although Britain is expected to grow more strongly than any of the other Group of Seven economies this year, many rich countries have already recovered their pre-recession size.
Britain's slow recovery is partly because of the size of its banking sector, which took a huge hit in the financial crisis. But critics say it is also because the government opted for sharp curbs on public spending.
The opposition Labour party has switched its line of attack away from the government's failure to revive growth to what it calls the cost of living crisis.
Britain's population has grown since the financial crisis, meaning that output per head is still well below pre-crisis levels, and driving a decline in real wages that is only just starting to level out.
Floods in many areas of Britain in February appeared to have had little effect on overall growth, although construction was hit by bad weather in January and February, the ONS said.
Output in services - which make up more than three quarters of GDP - rose by 0.9% in the first quarter after growing by 0.8% in the last quarter of 2013. That was the sector's fastest growth since the third quarter of 2012.
Industrial output was 0.8% higher - its strongest growth since the second quarter of 2010. Construction, which accounts for about 6% of GDP, grew by 0.3%.
George Buckley, an economist with Deutsche Bank, said it was encouraging that all three sectors were expanding.
"We expect growth to ease to something more sustainable during 2014," Buckley said in an email to clients.
Despite the strong growth, the Bank of England has signalled that it is in no rush to raise interest rates and its stance has been helped by the lowest consumer inflation rate in more than four years.
The Bank has welcomed a previously announced pickup in business investment as a sign that the recovery might be able to reduce its reliance on unsustainable consumer spending.
