This follows a 15.6% rise in house sales in August.
The Building Societies Association also showed a marked uplift in the number of people who say that now is a good time to buy a property — 37% in September, compared to 25% in June.
The increase in transactions came after the Chancellor introduced a temporary stamp duty holiday for residential properties worth up to £500,000 at the start of July, that will last until March next year.
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According to the government, the holiday means nine out of 10 people getting on or moving up the property ladder will pay no SDLT at all.
Chancellor Rishi Sunak said: “With a third of Brits planning to spend savings from the tax break on home improvements and renovations, the temporary stamp duty cut is boosting business and protecting jobs.
“This ranges from carpenters to cleaners, brickies and decorators, they can all benefit from each sale — helping us to further deliver on our Plan for Jobs.”
The stamp duty tax holiday was implemented to support hundreds of thousands of jobs in the housing sector and wider supply chain.
The Home Builders Federation estimates that 240,000 people are directly employed by housebuilders and their contractors, and the sector supports a further 300,000-500,000 people indirectly employed.