The government has announced a £9.9bn boost to the economy as a result of the Olympic Games.
The 'detailed' UKTI report on which these numbers are based suggests this breaks down to include £5.9bn of additional overseas sales and a £2.5bn boost in inward investment. Unfortunately, it provides no information on how these figures are calculated. It is certainly not possible to figure out whether they are in any sense additional (i.e. would not have happened if the games had not taken place).
One thing we can do, to start to figure this out is to look what happened to the overall balance of UK trade in that period:
To my eyes, there is little evidence of a trend change around the time of the Olympics (individual components don't look much different as you can see from the original report).
In short, you should take these numbers with a pinch of salt. If anyone knows of more rigorous analysis I'd be happy to receive a pointer.