The latest Markit/CIPS service sector purchasing managers index (PMI) fell to 53.3 last month from 55.6 in August.
Although above 50, indicating growth, it was the lowest figure since April 2013 as global uncertainty and weak UK manufacturing weighed on businesses.
Service sector growth in the third quarter slowed to a two-year low.
Markit said that its survey data indicated that UK GDP growth slowed to 0.5% in the third quarter of the year, and is entering the fourth quarter at a pace of 0.3%. This compares with growth of 0.7% in the second quarter of the year.
The service sector is of key importance to the UK as it accounts for about three-quarters of the economy.
Chris Williamson, chief economist at Markit, said: "Weakness is spreading from the struggling manufacturing sector, hitting transport and other industrial-related services in particular.
"Wider business service sector confidence has meanwhile also been knocked by global economic worries and financial market jitters."
He added the survey suggested shoppers were more cautious, pulling back on their leisure spending on restaurants and hotels.
The pound dropped slightly against other currencies, as the weak PMI reading suggested that the prospects of an early UK rate rise were diminishing. The Bank of England's monetary policy committee meets for its latest rate decision later this week.
David Tinsley, an economist at UBS, said: "If this is an accurate reading of the trajectory of the economy, it increasingly appears that UK growth has taken a marked step down."
He added that global uncertainty was "likely only part of the story" for the low service sector growth.
"The services PMI has been easing for some time, and the UK index has fallen by more than it has in the eurozone for example."
Other data released on Monday from Markit showed the eurozone composite PMI - which covers all business sectors - dropped to 53.6 in September from 54.3 the month before.
Although growth decelerated in Ireland, Germany, Spain and Italy, new orders and higher output created more jobs in the euro bloc.
Growth in the UK service sector slowed further in September to its lowest rate in nearly two and a half years, a survey has indicated.