The headline activity index of the Markit/CIPS purchasing managers' survey out on Thursday came in at 53.3 for May, the same as in April and above expectations for an easing to 52.5.
But a breakdown of the components painted a mixed picture of the sector.
Even though the new business index rose to 54.8, its highest since January, business expectations were at their lowest since December as firms fretted about public sector spending cuts and the euro zone debt crisis.
And the headline activity index, though remaining above the 50-point level that separates expansion from contraction, is still 3-4 points below its long-run average before the financial crisis.
An unexpectedly weak survey of manufacturing last week, coupled with grim jobs data from the United States and the escalating crisis in the euro zone, had fuelled bets the Bank
could restart its asset purchase programme.
The factory PMI fell to a three-year low of 45.9 in May, prompting a couple of major investment banks to dust off their calls for more QE. A Reuters poll before the factory PM I showed analysts saw only a 25 per cent chance of more QE in June.
Thursday's data could temper those QE expectations, although the composite PMI index, which combines the manufacturing, services and construction sectors, fell almost a point to 52.3 in May.
It's hard to get away from the fact that the UK economy remains relatively fragile," said Markit economist Paul Smith.