The Markit/CIPS headline services PMI index nudged up to 53.9 last month from a three-month low of 53.8 in May. That was above the 53.5 that economists had forecast but below its long-run average.
Taken alongside data in the past week showing a drop in manufacturing growth and a subdued construction sector, the figures suggest Britain's recovery failed to gain traction in the second quarter.
Chris Williamson, Markit's chief economist, predicted second-quarter GDP growth of 0.3 per cent at best, noting that services growth appeared to have slowed to 0.5 percent, from 0.8 percent in the first three months of the year.
"Worries over the impact of government austerity measures continue, and a number of panellists were pessimistic about economic conditions in general," the survey noted.
The only bright spot was on the inflation front. Input prices and prices charged both increased at their slowest pace this year, providing hope that inflation in the broader economy - currently more than double the Bank of England's two per cent target - will start to ease.
Britain's economy expanded by 0.5 per cent in the first three months of the year, a disappointing performance that only made up for the drop in the final three months of 2010.
The details of the PMI survey painted a subdued picture. Employment was static, new business growth slowed and confidence slipped to its lowest since October.
Reluctant to jeopardise Britain's fragile recovery, the central bank looks set to keep interest rates at a record low not just this week but for the rest of the year.
Investors are not fully pricing in a rise in UK rates until next June.