Fears about the health of the global economy have intensified following downbeat news about service sector activity in China, the eurozone and the UK. Share prices fell in Asia and the pound dropped to a 12-week low against the US dollar after fresh signs of weakness in China triggered speculation that its post-lockdown recovery was running out of steam. Meanwhile, there were signs the steady rise in interest rates is leading to weaker service sector activity in both the UK and the 20-country eurozone. Markets were particularly rattled by news…