Markit Economics said its services Purchasing Managers Index dropped to 52.3 from 53.7.
While that is above the 50 level that divides expansion from contraction, it’s the weakest since February 2013.
The slump follows bigger-than-expected declines in Markit’s manufacturing and construction surveys earlier this week.
The reports indicate growth of 0.1% in April, down from 0.4% in the first quarter.
Sterling nonetheless strengthened for the first time in five days against the euro, gaining 0.5% to 78.83p.
The index, which covers businesses from banks to hotels, has been above the 50 mark denoting growth for more than three-and-a-half years.
However, some panellists reported political instability had led to delays in getting contracts confirmed.
The uncertainty helped push the sub-index measuring new business to a 26-month low of 60.2 from 61.7 in March.
In Ireland, the Investec Purchasing Managers’ Index showed the lowest rate in more than two years in April, as uncertainty at home and abroad weighed on new business, analysts said.
The latest survey of consumers showed their confidence rose marginally in April, “suggesting that Irish consumers are not gripped by a newly returned pessimism”, KBC Bank and the ESRI think tank said.
Bank of England officials say they will interpret economic data around the referendum with caution.
The nine-member Monetary Policy Committee will announce its next interest rate decision and publish new forecasts next Thursday.
The Bank of England has already said the buildup to the June 23 vote is weighing on confidence and investment, and warned the impact could be more severe if the UK votes to leave the bloc in a so-called Brexit.
“Uncertainty about the EU referendum caused customers to hold back on purchases, exacerbating already-weak demand,” said Chris Williamson, chief economist at Markit in London.
In a separate report yesterday, Moody’s said that uncertainty over the referendum had pushed up funding costs for British lenders this year.