LONDON/TOKYO (Reuters) -Factories in the euro zone remained mired in contraction last month, surveys showed, with the data suggesting a recovery could be some way off but Asian and British manufacturers showed tentative signs of recovery.

However, analysts say prospects of slowing U.S. growth, which is likely to lead to interest rate cuts by the Federal Reserve this month, and uncertainty over the outcome of the presidential election there cloud the trade outlook.

HCOB's final euro zone manufacturing Purchasing Managers' Index (PMI), compiled by S&P Global, stood at 45.8 in August, just ahead of a 45.6 preliminary estimate but well below the 50 mark separating growth from contraction.

"The final August manufacturing PMI reading was yet another indication the recovery of the industrial sector will neither be immediate nor vigorous, as the euro zone index remains stuck in contractionary territory," said Riccardo Marcelli Fabiani at Oxford Economics.

A PMI covering new orders sank to its lowest since December and demand from abroad also fell at the fastest rate this year.

That decline came as euro zone manufacturers raised their prices for the first time in 16 months, driven by factories in France, the Netherlands, Greece and Italy.

Still, overall inflation in the currency bloc fell to a three-year low of 2.2% in August, preliminary official data showed on Friday, strengthening the case for further policy easing from the European Central Bank.

It will cut its deposit rate twice more this year, in September and December, according to more than 80% of economists in an August Reuters poll, fewer reductions than markets currently expect.

The downturn in German manufacturing accelerated and in France activity contracted at the fastest pace since January.

But in Britain factories had their strongest month in more than two years as demand at home offset a fall in exports, adding to signs of momentum in the economy.

That poses a favourable backdrop for the new government of Prime Minister Keir Starmer who is seeking to speed up growth.

CHIPS

Asian chip makers benefited from firm demand but economic headwinds pose a risk to the region.

China's Caixin/S&P Global manufacturing PMI rose to 50.4 in August from 49.8 in July, beating analysts' forecasts.

The reading, mostly covering smaller, export-oriented firms, shows a more optimistic view than an official PMI survey on Saturday, which indicated an ongoing decline in manufacturing activity.

"The PMIs for August suggest economic momentum held broadly steady last month, with modest improvements in manufacturing and services helping to offset a further slowdown in construction activity," Gabriel Ng, assistant economist at Capital Economics, said in a research note on China's PMI.

"But with factory gate price declines accelerating, the economy clearly remains at risk of slipping back into deflation," Ng said.

Factory activity in South Korea and Taiwan also expanded in August, while Japan saw a slower rate of contraction due in part to solid global demand for semiconductors.

Japanese manufacturers also gained from a rebound in car output after a safety scandal led some plants to temporarily suspend production.

But manufacturing activity contracted in Malaysia and Indonesia, surveys showed, underscoring the pain some of the region's economies are facing from China's prolonged slowdown.

"Chip-producing countries are doing fairly well, but China's slowdown will continue to drag on Asia's manufacturing activity for quite some time," said Toru Nishihama, chief emerging market economist at Dai-ichi Life Research Institute.

"Slowing U.S. demand could add to the pain on Asian economies, many of which are already wary of the fallout from sluggish Chinese growth," he said.

Japan's final au Jibun Bank Japan manufacturing PMI rose to 49.8 in August, in contractionary territory for a second month but less sharply than in July.

South Korea's PMI stood at 51.9, up from 51.4 in July, in part due to strong customer confidence and new orders in the domestic market. Malaysia's PMI held at 49.7 while Indonesia's fell to 48.9.

India's manufacturing activity growth eased to a three-month low as demand softened significantly, casting another shadow over the otherwise robust economic outlook.