Markit's and the Chartered Institute of Purchasing & Supply's services purchasing managers' index (PMI) for the U.K. jumped to 58.5 in June from 56.5 in May, exceeding expectations for a rise to 57.4.

A reading above 50 indicates expansion in the sector.

The increase was driven by robust expansion in new work inflows.

"While uncertainty caused by the Greek debt crisis rules out any imminent hike in interest rates, the post-election rebound in service sector business activity adds to the likelihood of the Bank of England starting to nudge rates higher later this year. The survey data are indicating an acceleration of economic growth to 0.5% in the second quarter, up from 0.4% in the first three months of the year," the Chief Economist at Markit Chris Williamson said.