The Markit/CIPS PMI services index said the rise was due to growth in financial services, bolstered by the housing market, and the business sector.
The survey raises hopes that the economy as a whole saw strong growth in the July-to-September period.
The PMI survey showed services continued to grow strongly last month.
The activity index for the sector recorded 60.3 in September, which was marginally down from August’s near seven-year high of 60.5. Any score above 50 indicates growth.
The strong reading for the UK services sector follows similarly strong surveys of the manufacturing and construction sectors published earlier this week.
David Noble, chief executive officer at the Chartered Institute of Purchasing & Supply, said: “After nearly six lost years of economic output, the UK economy looks to have really found its feet.”
He said the survey reflected the stability in the global economy, which the services sector was taking “full advantage of”.
“The industry sustained August’s impressive business growth, dipping only fractionally from a near seven-year high, and new orders have now been growing for nine months consecutively,” Mr Noble added.
Chris Williamson, chief economist at Markit, said there were “encouraging signs” that growth would continue in the coming months.
“September saw one of the largest inflows of new business ever seen by the services survey,” he said.