The 50.2 reading in the Markit/CIPS purchasing managers index (PMI) was above the 50 mark which signals expansion but below the 50.6 recorded in October.
Confidence in the sector dipped in November to the lowest seen in 2012 due to worries over the direction of the economy and public sector spending cuts.
Respondents to the research said demand is weak with clients generally holding back on spending wherever possible.
Levels of new work declined slightly – the first fall since December 2010 – although there was a marginal increase in employment.
Chris Williamson, chief economist at survey compiler Markit, said there appeared to be little chance of a quick upturn in the services sector.
He said: "With the exception of December 2010, when the country suffered heavy snowfall, the sector's performance was the worst since early-2009, with companies reporting a pull-back in expenditure on services by both cor-porate customers and households."
The services sector performance, coupled with a similarly downbeat performance in the construction and manufacturing sectors earlier this week, has revived fears UK GDP may go into reverse after jumping 1% quarter-on-quarter in the three months to September.
Howard Archer, chief economist at IHS Global Insight, said: "We had expected the economy to be essentially flat in the fourth quarter, but there currently seems to be an ever-increasing risk that a renewed dip in GDP could occur.
"If the economy is to avoid a renewed GDP dip in the fourth quarter it is going to need robust consumer spending through December as well as a pick-up in services activity."
Vicky Redwood, at Capital Economics, said: "The further deterioration in the UK CIPS/Markit report on services suggests the recovery in the biggest part of the economy has completely fizzled out. The outlook for growth next year is clearly looking shaky."
Mr Williamson added: "Coming on the back of disappointing surveys of manufacturing and construction, the UK CIPS/Markit purchasing managers index adds to worrying signs that the economy faces a renewed slide back into contraction after the temporary growth surge seen in the recent third quarter."