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 per cent 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 per cent, picking up a bit from growth of 0.7 per cent in the last three months of 2013, the ONS said.
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 per cent smaller than at its peak in the first quarter of 2008 after the recession wiped 7.2 per cent off total output, the ONS said.
But excluding the oil and gas sector, which is in decline, output was 0.3 per cent 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.
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.
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 per cent in the first quarter after growing by 0.8 per cent in the last quarter of 2013. That was the sector's fastest growth since the third quarter of 2012.
Industrial output was 0.8 per cent higher - its strongest growth since the second quarter of 2010. Construction, which accounts for about 6 per cent of GDP, grew by 0.3 per cent.
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.