The GDP figure is much higher than the 0.6% predicted by City experts. Between January and March, the economy grew by just 0.3%.
Overall, the UK posted its strongest annual growth - 1.6% - since before the recession at the beginning of 2008 during the second quarter.
The huge advance was driven by the services sector which accounts for three-quarters of the economy and saw its best quarter in more than three years with growth of 0.9%.
There was also a big contribution from the construction industry, which grew at its fastest pace since 1963.
The 6.6% rise over the quarter contributed 0.4 percentage points to overall GDP, as building bounced back from a snowbound first three months of the year.
The news provided the pound with a large boost on Friday - at one point it traded at around 2 cents up against the dollar at £1.54 and 1 euro cent up against the single European currency at £1.19.
Despite this positive news, experts are warning the growth could be as good as it gets for a while as Chancellor George Osborne's strict Budget cuts start to take effect.
Mr Osborne said: "Today's figures show the private sector contributing all but 0.1% of the growth in the second quarter, and put beyond doubt that it was right to begin acting on the deficit now.
"While I am cautiously optimistic about the path for the economy, the job is not yet done.
"The priority now is to implement the Budget policies which support rebalancing and help ensure the sustained growth that the Office for Budget Responsibility forecast this year and next."
The strong performance will also put pressure on the Bank of England's Monetary Policy Committee to consider a rise in interest rates from their record low of 0.5%.
Alistair Darling MP, Labour's shadow chancellor said: "Today's figures show the results of the Labour Government's approach to supporting the recovery.
"This is the fastest growth we have seen for over four years. It shows that confidence was returning. And you can see the success of maintaining support for important sectors like construction.
"And this is the final nail in the coffin of the Coalition's argument that things are worse than they believed before the election.
"They will have to accept responsibility for the risks they are taking with the economy."
