Volume sales were up 12.5% on the same period a year earlier boosted by the hot summer and the Budget beer tax cut, the BBPA said.
It estimated that the Treasury collected £16 million in beer taxes because of the increase, despite the cut in duty rates.
The on-trade was down 1.2% but total beer sales were up 5.2%, the biggest quarterly increase this century.
BBPA chief executive Brigid Simmonds said: “After many years of disappointing figures it’s great to see a great British product reporting such a strong third quarter performance.
“There is a still a way to go, but with increased investment and a fairer tax regime, we can build for future success.
“With the beer duty escalator cancelled by George Osborne, and tax revenues up, there is a real opportunity, if we have another freeze next year.”