The closely watched Markit/CIPS services purchasing managers’ index (PMI) showed a reading of 51.7 in March, down from 54.5 in February.
It is the weakest service sector performance since July 2016, according to the survey.
Businesses were disrupted by unusually bad including snow last month, which contributed to lower consumer spending.
“Heightened economic uncertainty” also affected the service sector, acting as a “brake on growth”, the report said.
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It marks further bad news for the UK economy after separate PMI data earlier this week showed a contraction in the construction sector and only a marginal month-on-month improvement in manufacturing.