But the Chartered Institute of Purchasing and Supply, publishing the survey yesterday, calculated that its monthly services, manufacturing and construction reports together pointed to UK gross domestic product growth of at least 0.7% in the first quarter.
CIPS's business activity index for services dipped from 58.2 in February to 57.6 in March on a seasonally adjusted basis, remaining well above the level of 50 deemed by CIPS to separate expansion from contraction but signalling the slowest growth in the sector in nine months.
And growth of employment in services eased in March to its slowest pace in six months.
CIPS's latest survey of the UK manufacturing sector, published on Tuesday, showed its growth eased for a fourth consecutive month in March to its slowest pace since last summer.
The latest report on the construction sector from CIPS showed that its growth eased marginally in March but remained sharp. This recovery in construction activity follows a grim period.
Chris Williamson, chief economist at CIPS survey compiler Markit, said of the latest purchasing managers' index surveys: "The March PMI surveys signalled a strong end to what looks to have been another quarter of above-trend economic growth of at least 0.7%.
"Growth may weaken from here, but only modestly with no sharp easing in sight."
CIPS's services survey showed growth in new business eased to its slowest pace in 10 months in March, although it remained strong by historical standards.
Services companies' optimism about levels of activity in 12 months' time eased to its lowest level in four months in March.
Samuel Tombs, UK economist at consultancy Capital Economics, said: "The further deterioration in the tone of the CIPS/Markit services survey in March shouldn't ring too many alarm bells about the strength of the economic recovery."
He added: "Admittedly, the drop in the headline activity index took it to a nine-month low. The future activity and employment indices also eased a touch. But these balances have weakened from very strong levels. On the basis of past form, the activity index is still consistent with quarterly growth in the official measure of services output of about 1%."
Howard Archer, chief UK economist at consultancy IHS Global Insight, said: "A modestly softer survey for the services sector follows on from the purchasing managers also reporting a slight weakening in manufacturing and construction [growth] in March.
"This fuels our suspicion that, while the UK economy is still performing pretty well, activity has recently lost a little momentum. Overall, the … surveys tie in with our view that GDP growth is likely to ease back to a still healthy 0.6% to 0.7% quarter-on-quarter range from the 0.7% to 0.8% range seen during the final three quarters of 2013."