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Markit's and the Chartered Institute of Purchasing & Supply's services purchasing managers' index (PMI) for the U.K. rose to 53.7 in March from 52.7 in February, in line with expectations.
A reading above 50 indicates expansion in the sector.
The increase was driven by a faster growth in output. Employment continued to rise in March.
"An upturn in the pace of service sector growth in March was insufficient to prevent the PMI surveys from collectively indicating a slowdown in economic growth in the first quarter. The surveys point to a 0.4% increase in GDP, down from 0.6% in the closing quarter of last year," the Chief Economist at Markit Chris Williamson said.