By Jonathan Cable and Leika Kihara

LONDON/TOKYO (Reuters) - European manufacturers may be over the worst of a coronavirus-driven downturn, but Asia's pain deepened in May due to a slump in global trade, with export powerhouses Japan and South Korea seeing the sharpest falls in activity in over a decade, surveys showed.

The new coronavirus pandemic - which has killed more than 370,000 people around the world - has wreaked havoc with supply chains and quashed demand as government-imposed lockdowns forced businesses to close and citizens to stay home.

While factory activity still contracted sharply across Europe last month, purchasing managers said April lows had passed as governments on the continent began to ease the tough lockdown measures implemented to contain the spread of the virus.

After crashing to its lowest reading in the survey's nearly 22-year history in April, IHS Markit's Manufacturing Purchasing Managers' Index (PMI) for the euro zone recovered somewhat last month, rising to 39.4 from 33.4.

But that was still a long way from the 50 mark separating growth from contraction, something echoed in surveys from other countries in the region.

"There was a clear sense that - particularly in the euro zone - April was likely to be the bottom of the trough. Hopefully we are past the worst," said Peter Dixon at Commerzbank.

Britain also saw another sharp downturn and pockets of growth were mostly linked to healthcare and personal protection equipment although some firms reported signs of new inflows of business as clients began to reopen.

Later in the day, data from the United States is expected to show factory activity declined there again last month.

Alongside the devastating impact of the pandemic, a U.S.-China spat over Hong Kong's status and Beijing's handling of the pandemic could sour business sentiment and add to already huge strains on the global economy.

So the trough in global economic activity will be deeper and the rebound is likely to take longer than previously predicted as the pandemic spreads in waves, a recent Reuters poll found.

The International Monetary Fund said last month the global economy would take much longer than expected to recover fully from the virus shock, suggesting a downgrade to its current projection for a 3% contraction this year.

Still, world stocks were just shy of three-month highs on Monday as optimism on economies opening up boosted risk appetite, despite worries over riots in the United States and lingering unease over Washington's standoff with Beijing.