The headline reading of 58.2 in the closely watched Markit/CIPS purchasing managers' index (PMI) was the lowest since June but still came in well ahead of the level of 50 that separates growth from contraction.
Growth has now been recorded for 14 months and the latest increase in output was supported by another marked rise in new business. Confidence in the outlook also strengthened to the highest for nearly four-and-a-half years.
The survey found that adverse weather in some parts of the UK disrupted activity but that the relatively mild winter had also provided a support to growth.
Alongside good performances in PMI manufacturing and construction, Markit said the upbeat picture of the services economy points to the UK enjoying another quarter of robust economic growth of approximately 0.7%.