LONDON, Sept 23 (Reuters) - Europe's economy is showing unexpected signs of health even as conflicts in the Middle East and Ukraine drive up energy costs for firms and households, key business surveys showed on Wednesday.

Business activity across the euro zone accelerated in September at its fastest rate in over three years, S&P Global said, with solid growth registered across both the manufacturing and service sectors.

The S&P Global Flash Euro Zone Composite PMI Output Index — where readings above 50.0 signal an expansion in activity — jumped to 53.1 in September from August's 52.0, defying expectations in a Reuters poll for a dip to 51.7. The highest forecast in the poll was for 52.6.

"All in all, today’s PMI readings are almost too good to be true," said Carsten Brzeski at ING. "A euro zone economy that remains completely unharmed by an energy price shock and supply chain disruptions is a welcome surprise. Let’s hope it doesn’t turn out to be a mirage."

S&P said the latest rise in output was broad based across geographies covered by its data.

Business activity in Germany, Europe's largest economy, expanded solidly in September despite firms facing increased inflationary pressures while in France it grew at its fastest pace in just over two years, driven by a rebound in services demand.

But in Britain, outside the European Union, growth cooled this month as inflation pressure built, its PMI showed, an awkward backdrop for finance minister John Healey ahead of his first budget next month.

Overall new orders in the currency union surged at their fastest pace in over four years supported by a further rise in exports — which include intra-euro zone trade.

The bloc's services PMI bounced to its highest in nearly a year and was well ahead of estimates for a fall, while the manufacturing index held steady.

A gauge of output - which feeds into the composite PMI - nudged higher.

To meet the rise in demand firms took on more staff but faced a jump in input costs due to elevated energy prices stemming from the US war with Iran. They were able to pass some of this on to customers.

"September’s big improvement in the euro zone’s composite PMI supports our view that despite the weakness in the official activity data in July, GDP will increase in Q3," said Jack Allen-Reynolds at Capital Economics. "The output price PMIs rose too, but there is still no sign of 'second-round' effects on wages."

Earlier this month the European Central Bank raised interest rates for the second time this year to quell an energy-driven inflation rise and warned price pressures could prove lasting.

Markets are pricing three more ECB rate hikes by the end of June 2027.

"Today's PMI readings make it more difficult for even the ECB's most dovish policymakers to rule out another rate hike," said ING's Brzeski.

(Reporting by Jonathan Cable; Editing by Toby Chopra)