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Markit's and the Chartered Institute of Purchasing & Supply's services purchasing managers' index (PMI) for the U.K. rose to 55.9 in November from 54.9 in October, exceeding expectations for a rise to 55.0.
A reading above 50 indicates expansion in the sector.
The increase was driven by a faster growth in new business and a moderate rise in backlogs.
"A welcome upturn in service sector expansion helped counter slower growth in manufacturing and construction in November, suggesting the UK continues to enjoy the 'Goldilocks' scenario of solid economic growth and low inflation," the Chief Economist at Markit Chris Williamson said.
He added that the U.K. economy is likely to expand 0.6% in the fourth quarter of 2015.