Data from the closely watched Markit/CIPS purchasing managers' index (PMI) showed that the sector - representing three-quarters of output - recorded a reading of 57.6 in March, where the 50 mark separates growth from contraction.
It marked a fall from the 58.2 recorded in February and its lowest reading since June last year.
The figures follow data earlier in the week showing growth also slowed marginally in manufacturing and construction, leaving the all-sector PMI at a nine-month low of 58.1.
This indicates that while the sectors continue to show robust improvement, the pace has slackened off. Overall economic output is still below its pre-crisis peak at the start of 2008.