The figures are unlikely to alter expectations that the Bank of England will keep its ultra-loose policy stance unchanged later this week and probably well into next year.
The headline index of the Markit/CIPS services PMI index increased to 52.8 from 51.3, versus economists' expectations for a slight fall to 51.0.
However, planned cuts to government departments' spending of around a quarter over the next five years already seem to be affecting the firms covered in the survey, which excludes most activity in the public and retail sectors.
"Inflows of new work and prospects for the year ahead have been hit by widespread worries that the recovery is losing steam, cancelled government contracts and the prospect of more cuts to come," said Markit's chief economist, Chris Williamson.
The new business component slowed to a 15-month low of 51.3 from 51.4. Business expectations for the coming year increased to a four-month high but remained subdued by historic standards.
"Unless trends in new business show an improvement soon, the lack of confidence is consistent with a downturn in business activity in the coming months," Williamson said.
Markit said that third-quarter service-sector output was the weakest since the second-quarter of 2009. This bodes ill for third-quarter GDP growth, which economists already expect to slow sharply from a nine-year high of 1.2 per cent in the second quarter as temporary factors fade and spending cuts bite.
The Office for National Statistics reported 0.2 per cent monthly falls in output for the entire service sector – which makes up around three quarters of Britain's economy – for June and July.
The PMI survey points to some easing in the inflation pressures which has made the Bank of England's Monetary Policy Committee wary of further loosening monetary policy up to this point.
The prices charged index fell for the first time since March. But this may prove to be a temporary dip, as firms' costs rose at the fastest pace since May, due to higher fuel, utility and food costs.