(Updates with latest moves, milestones and analyst comment) LONDON, July 8 (Reuters) - Sterling on Thursday fell to its lowest against the euro in more than three weeks and eased further against the dollar amid a broader shakeout in FX markets that saw riskier currencies fall and safe havens gain. The pound took a beating along with other risk-correlated currencies such as the Australian and New Zealand dollars that fell in the wake of minutes of the last Federal Reserve meeting that confirmed its policymakers were moving towards tapering the central bank’s asset purchases as soon as this year. “Cable had a tentative attempt to stay above $1.38 yesterday but has lost this level today as risk aversion dominates,” said Roberto Cobo Garcia, FX strategist at BBVA. Adding to sterling’s woes on the day was the European Central Bank’s setting a new inflation target, which gave the euro a broad boost. Sterling sank to 86.18 pence per euro by late afternoon trade, its lowest levels against the single currency since June 15. “Sterling is also losing ground against the euro due to its higher-beta nature ahead of tomorrow’s set of UK macro releases,” Garcia said, adding that industrial production and May’s monthly GDP may prove to be important for the pound’s short-term direction. Against the dollar, sterling traded 0.3% lower on the day at $1.3758 by 1535 GMT. Sterling has found some support this week on British Prime Minister Boris Johnson’s plans to end social and economic COVID-19 restrictions in England. But investors remain cautious as the government also warned that the number of coronavirus cases could climb as measures are relaxed. British house prices saw their most widespread rises since 1988 last month, but fewer homes were put up for sale and buyer demand grew less quickly ahead of the end of a tax break on property purchases, an industry survey showed. Reporting by Ritvik Carvalho Editing by Mark Heinrich, William Maclean Our Standards: The Thomson Reuters Trust Principles.