The reading of 60 for November in the Markit/CIPS purchasing managers' index (PMI) was comfortably ahead of the 50 level which separates growth from contraction.
Although it was a dip from a 16-year high of 62.5 in October economists suggested the result was another indication of the UK's economic recovery beginning to build.
Martin Beck, from Capital Economics, believes the services report and strong survey results from construction and manufacturing in recent days suggest there should be a solid GDP rise in the fourth quarter.
He said: "A weighted average of the three CIPS surveys still points to quarterly GDP growth in Q4 of around 1.5%.
"Admittedly, the CIPS surveys have tended to present a rosier picture of the economy than the official data in recent quarters. And the recovery in the retail sector, which the CIPS survey does not cover, has shown signs of cooling.
"But, for now, there is a good chance that quarterly GDP growth in the final three months of the year will beat the 0.8% rate recorded in [the third quarter]."
In the services PMI job creation surged while backlogs of work for an eighth month in a row.
Investment levels are forecast to increase with companies planning to hire additional staff, launch new products and expand into more territories.
Chris Williamson, chief economist at Markit, said: "Although signalling an easing in the rate of growth in November, the PMI survey of the services economy continues to signal an impressively strong pace of expansion and one of the best performances for the sector we've seen since data were first collected in 1996."
On a more cautionary note operating costs rose at the sharpest pace since February with higher utility prices and wage bills among the factors cited.
But the expectation is the services sector will continue to grow into 2014.
Howard Archer, from IHS Global Insight, said: "The survey shows incoming new services business in November almost matching October's record high which bodes well for further robust services activity in the near term at least."