The pound fell in the wake of the survey's publication yesterday, as financial markets took the view that a slowdown in services growth could push back the timing of the first rise in UK base rates from their record low of 0.5%.
But the Chartered Institute of Purchasing and Supply, which conducts the services survey in conjunction with financial information company Markit, emphasised that the sector's rate of expansion remained sharp by historical standards.
CIPS's business activity index for services fell from 60 in November to 58.8 in December on a seasonally-adjusted basis. It had stood at 62.5 in October.
The rate of new business growth for UK services companies also slowed in December, according to CIPS, although it also remained sharp. The survey showed an acceleration of the pace of increase in employment in the service sector.
And services companies were at their most confident last month since March 2010.
CIPS said that the computing and information technology, transport and communication, financial services and business- to-business services sub-sectors had enjoyed the strongest expansion during the fourth quarter of last year.
It highlighted hotels and restaurants and personal services as the weakest sub-sectors.
Chris Williamson, chief economist at Markit, said: "While these household-facing sectors have nevertheless seen decent growth, their under-performance is another reminder that this is not purely a consumer and housing-driven boom that we are currently seeing."
A survey published last week by CIPS showed that growth in UK manufacturing activity slowed in December, but remained sharp as the sector continued to mount a recovery, following a difficult five years.
CIPS said last week that growth in the UK construction sector had slowed slightly in December.
Samuel Tombs, UK economist at consultancy Capital Economics, said: "Although the CIPS services survey softened again in December, it still suggests that the recovery was strong at the end of 2013. And with the survey showing confidence rising and new business growing strongly, 2014 is shaping up to be another year of strong growth."
He added: "Like the manufacturing and construction surveys already released, the CIPS services survey weakened a touch in December... However, the index was still consistent, with a very strong rate of growth."
Howard Archer, chief UK economist at consultancy IHS Global Insight, said: "There will obviously be some disappointment that the purchasing managers' survey showed services activity moderating to a six-month low in December, but this needs to be put into perspective."