Markit's and the Chartered Institute of Purchasing & Supply's services purchasing managers' index (PMI) for the U.K. rose to 53.5 in May from 52.3 in April, exceeding expectations for an increase to 52.5.

A reading above 50 indicates expansion in the sector.

The increase was driven by a faster growth in output. Employment continued to rise in May.

"The PMI surveys show that the pace of economic growth remained subdued in May, as 'Brexit' worries exacerbated existing headwinds. The data so far indicate that the second quarter is likely to see the economy grow by just 0.2%," the Chief Economist at Markit Chris Williamson said.