The Markit/CIPS Purchasing Managers' Index (PMI) for the sector rose to 53.5 last month from 52.3 in April. A figure above 50 indicates expansion.
More than a third of firms said they had suffered from the uncertainty over the EU referendum, Markit said.
It added the economy was likely to grow by 0.2% in the second quarter of 2016.
That would be a slowdown from the 0.4% growth recorded in the first three months of the year.
PMI surveys released earlier this week indicated the manufacturing sector edged back into growth during May, while activity in the construction sector slowed.
Markit chief economist Chris Williamson said: "The PMI surveys show that the pace of economic growth remained subdued in May, as 'Brexit' worries exacerbated existing headwinds.
"Growth has collapsed in manufacturing and construction, leaving the economy dependent on the service sector to sustain the upturn, though even here the pace of expansion has remained frustratingly weak so far this year."
The Markit/CIPS survey found new business in the service sector grew at its slowest pace for 41 months.
Job creation also slowed to its weakest pace since August 2013. Markit said this largely reflected "lacklustre inflows" of new business, while some firms said the new National Living Wage had affected hiring.
"Despite some improvement compared to April, this is still a pretty lacklustre survey that points to muted services activity," said Howard Archer, chief UK and European economist at IHS Global Insight.
"The muted services sector is particularly significant as the dominant sector was entirely responsible for UK GDP growth of 0.4% quarter-on-quarter in the first quarter."
Activity in the UK's dominant service sector picked up last month, according to a closely-watched survey, but growth remained "subdued".