By Jonathan Cable

LONDON, Aug 23 (Reuters) - Euro zone private business activity was stable in August, albeit at a muted level, but factories possibly face a tougher September as new order growth stumbled, a survey showed on Tuesday.

Muddying the outlook for the coming months is the United Kingdom's vote in late June to leave the European Union, although so far the economic repercussions seem to have been confined to Britain, not its main trading partner.

"Policymakers will be quite encouraged that it is moving in a positive direction. It looks cautiously optimistic for the region in the face of the Brexit threat," said Chris Williamson, Markit's chief economist.

Markit's flash composite Purchasing Managers' Index edged up to a seven-month high of 53.3 from July's 53.2, where any reading above 50 indicates growth. A Reuters poll of economists had predicted a slight dip to 53.1.

Williamson said the PMI pointed to GDP expanding 0.3 percent this quarter, matching a Reuters poll earlier this month that showed the euro zone economic outlook stable but lackluster, about half the speed at the start of the year.

Pressure remains on the European Central Bank to announce more easing as it has so far been unsuccessful in getting inflation anywhere close to its 2 percent target ceiling.

But there is little confidence amongst economists about just how much firepower the ECB has left. ECILT/EU

Of some concern, having only trimmed their prices in July, firms returned to deeper discounting this month. The output price index fell to 49.5 from 49.8.

Discounting helped drive a PMI covering the bloc's dominant service industry up to 53.1 from 52.9, also confounding expectations for a dip to 52.8. The manufacturing PMI was predicted to have held steady at July's 52.0 but fell to 51.8.

The factory output index, which feeds into the composite PMI, nudged up to an eight-month high of 54.0 from 53.9.

However, new order growth was at its weakest since early 2015, falling to 51.5 from 52.2, suggesting the headline manufacturing PMI may decline next month.

Service firms were also less optimistic about the year ahead. The business expectations index fell to 60.2 from 60.9, its lowest reading since late 2014.

"There are some warning lights flashing about the future," Williamson said.

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(Editing by Toby Chopra; ((jonathan.cable@thomsonreuters.com; +44 20 7542 4688; Reuters; Messaging: jonathan.cable.thomsonreuters.com@reuters.net)))