The Markit/CIPS Purchasing Managers Index (PMI) fell to 57.7 in June, from May's high of 58.6.
However, despite an easing growth rate, the data marked the eighteenth consecutive month of rising employment.
Furthermore, when combined with the manufacturing and construction PMIs, the all-sector index signals gross domestic product growth of 0.8 per cent in the second quarter.
Chris Williamson, chief economist at Markit, believes the economy's strength could bring unemployment down even further.
He said: "Alongside an ongoing surge in construction and the largest quarterly rise in manufacturing output for 20 years, the services PMI confirms that the economy is firing on all cylinders.
"We expect the economy to grow by 0.8 per cent again in the second quarter, taking GDP to a new all-time high.
"A renewed upturn in growth of new orders across all three sectors suggests that the economy should also pick up speed again as we move into the second half of the year."
He added: "With the survey having seen new record rates of job creation in each of the past three months, unemployment should continue to plummet in the second quarter from the 6.6 per cent rate seen in the first quarter.
"A jobless rate below six per cent is achievable by the end of the year if anything like the current pace of job creation is sustained in the coming months."
As a result of the recent growth some analysts have forecast an interest rate hike from the Bank of England by the end of the year.
Howard Archer, chief UK and European economist, IHS Global Insight, said: "While the services index eased back in June, this is still a strong reading as it is well above its lifetime average and substantially above the 50 level that denotes flat activity."
He added: "With Governor Mark Carney stressing that the strength of data will drive when the Bank of England will first edge up interest rates, the robust set of June purchasing managers' surveys with strong incoming new business will likely be seen as supportive to a move in late-2014 rather than early-2015.
"Not only do the surveys show ongoing strong activity and elevated incoming new business, but they also indicate a further marked rise in employment."