The survey, published yesterday by the Chartered Institute of Purchasing and Supply and compiled by financial information company Markit, also showed a pick-up in the rate of increase of the services sector workforce.
CIPS's headline business activity index for services rose from 57.6 in March to 58.7 in April, on a seasonally-adjusted basis, with the latest reading ahead of the consensus forecast of 57.6 among economists. The level of 50 is deemed by CIPS to separate expansion from contraction, so the April reading, which was only slightly adrift of the 58.8 figure for December 2013, continues to signal significant growth.
CIPS's employment index for the services sector rose from 53.5 to 56.
The rate of growth of new business for services companies eased further to its slowest pace in 11 months in April. But CIPS noted the new business index continued to signal a rate of increase which was sharp by historical standards.
CIPS's survey of services sector activity, which does not include retail, also showed an improvement in firms' confidence about their activity levels in 12 months' time to a point just adrift of the four-and-a-half-year high for optimism recorded in February.
A survey published on Friday by CIPS showed that growth in UK construction activity eased in April to its slowest pace since October 2013, but was still well ahead of the long-term average.
Meanwhile, CIPS reported last week that growth of UK manufacturing activity had accelerated sharply in April as firms hired employees at a rapid rate.
Markit chief economist Chris Williamson noted, taking CIPS's manufacturing, construction and services surveys together, the "all-sector" output index had risen to a five-month high of 59.4 in April from 58.2 in March.
He said that historical comparisons indicated that the April reading was consistent with the UK economy growing at a quarterly rate of 0.8%.
Figures published last month by the Office for National Statistics showed the UK economy had grown by 0.8% in the first quarter. However, UK GDP remained adrift of its level ahead of the 2008-09 recession in the first quarter.
Paul Hollingsworth, assistant economist at consultancy Capital Economics, said: "April's CIPS/ Markit Services report provided encouraging evidence that the domestic recovery retained a healthy degree of momentum at the beginning of Q2."
He added: "Overall, the latest CIPS/ Markit services survey adds to other evidence that the UK economy is experiencing a 'Goldilocks' scenario of solid GDP growth and low inflation. We continue to expect GDP to grow by around 3% or so in 2014."
Howard Archer, chief UK economist at consultancy IHS Global Insight, said: "A robust (services) purchasing managers' survey adds to the ongoing upbeat news on the UK economy. The survey reinforces the impression that the UK economy got off to a strong start to the second quarter."
He added: "While a near-term interest rate hike remains extremely unlikely, opinions within the Bank of England are likely to become more diverse over the coming months over exactly when monetary policy should start to be gradually tightened, and the more hawkish members (of the Monetary Policy Committee) may well start to favour a first small rate hike before the end of 2014. We maintain the view that interest rates are still most likely to start edging up in the second quarter of 2015.
"The Bank of England wants to give the economy every chance to develop sustainable, balanced growth, with business investment seeing extended improvement and exports increasingly kicking in."
David Noble, chief executive officer at CIPS, said: "Growth and momentum in UK services remained steadily bullish in April as activity increased at the fastest rate this year. Most encouraging of all has been the increase in job creation since last October, a reflection of positive prospects of market expansion. With business confidence rising further in April, firms seem convinced a long-term strong trend is set to continue."