In its quarterly economic forecast, the think tank upgraded its gross domestic product (GDP) forecasts for Britain to 2.9 percent for 2014, from earlier estimates of 2.5 percent, and to 2.4 percent in 2015, from 2.1 percent. The NIESR expects growth to remain around 2.4 percent per annum until 2017.
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"Growth has certainly accelerated quicker than most people - including us – were expecting. Although historically, recoveries in the U.K. have tended to progress with reasonable speed," Jonathan Portes, director of the NIESR, told CNBC.
As a result of this growth spurt, U.K. GDP will exceed its 2008 high "in the next few months," the NIESR said – significantly faster than its previous estimate of 2015. From peak to trough in 2009, the economy shrank by 7.2 percent, according to the Office for National Statistics (ONS).
In the first quarter of this year, Britain posted GDP growth of 0.8 percent quarter-on-quarter. But despite this marking the fifth quarter of expansion in a row, the ONS said GDP remained 0.6 percent below its pre-crisis peak.
By contrast, the U.S. economy is already around 6.3 percent bigger than it was at the end of 2007.
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"On the official figures, it wasn't the case that the U.K. economy made up the ground it lost since the crisis in the first quarter of this year, but it almost certainly will in the second," Portes said.
The NIESR also issued monthly GDP estimates on Friday, and said that output grew by 1.0 percent in the three months to the end of April - just 0.17 per cent off its pre-recession peak.
Portes added that, after revisions to official GDP data, it "could well be the case" that the economy actually exceeded its peak in the first quarter.