The National Institute of Economic and Social Research suggested GDP would be 0.8 per cent at the next reading.
NIESR said this was the "most robust" rate of growth since the three months to July 2010.
It followed growth of just 0.1 per cent in the three months ending in August 2012.
The thinktank said: "Unless output turns down again, the recession is over, while the period of depression is likely to continue for some time."
Recession is termed as falling output while depression is a period when output is depressed below its previous peak.
NIESR said it did not expect output to pass its early-2008 peak until 2014.
However, it said the growth was largely due to the effect of special events such as the Olympics and additional bank holidays.
It said: "The strength of the figure for the three months to September is largely an artefact of special events. Economic growth is expected to be at a significantly slower pace in the coming quarters."
The official GDP figures from the Office for National Statistics will be released on 25 October.
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