The Markit/CIPS services purchasing managers' index (PMI) stood at 52.6, down from August's 52.9, but above the 50 level which indicates expansion.
On Monday, the manufacturing sector recorded its best PMI for two years.
Markit said the latest findings cast doubt on the need for more stimulus action from the Bank of England.
The surveys, which are calculated by speaking to purchasing professionals and business decision-makers across a range of companies, are seen as an early indication of how the economy is performing, since they are released before official GDP data.
"The survey results suggest that the economy has regained modest growth momentum since the EU referendum, with especially strong growth appearing in manufacturing," said Markit's chief business economist Chris Williamson.
"The risk of recession in the second half of 2016 has therefore all but evaporated, and the solid PMI readings for September will cast doubt on the need for any further stimulus from the Bank of England in coming months."
July's survey had shown a steep drop in business activity in the immediate wake of the referendum, but that started to recover in August. In addition, September's survey indicated that new business in services rose at the fastest pace since February and that the rate of job creation had picked up.
However, Mr Williamson pointed out that the pace of expansion had cooled since the beginning of the year, "reflecting widespread concern about the potential future impact of Brexit".
Official growth figures for the second quarter were revised up to 0.7% last week, by the Office for National Statistics (ONS), from an initial reading of 0.6%.
Pantheon Economics agreed that the Bank of England would probably refrain from cutting rates in November but predicted growth would continue to slow in the coming months, "as firms hold back from hiring and investment due to 'hard' Brexit risk and households' real incomes are squeezed by rising inflation".
The PMI survey showed that services firms reported the fastest rate of input price inflation since February 2013 in September, with providers subsequently raising their charges at the fastest rate since January 2014.
The services industry - which includes everything from financial advice to retailers - accounts for about three-quarters of the UK economy.
The UK services sector continued to recover last month, after a sharp drop in activity following the Brexit vote, according to a closely watched survey.