(Adds Shanghai closing prices, updates London prices) HANOI, June 8 (Reuters) - Shanghai copper prices fell on Tuesday, as fears of monetary policy tightening in the United States and softer demand in top consumer China pressured prices. The most-traded July copper contract on the Shanghai Futures Exchange slipped as much as 0.8% to 71,100 yuan ($11,125) a tonne before closing 0.4% lower at 71,420 yuan. Three-month copper on the London Metal Exchange edged up 0.2% to $9,921 a tonne by 0717 GMT. U.S. Treasury Secretary Janet Yellen said this week President Joe Biden’s $4 trillion spending plan would be good even if it contributes to inflationary pressure and results in higher interest rates, Bloomberg News reported. “Data in the United States is starting to point towards inflation taking hold and Janet Yellen has made comments ... which sounds like a case of softening up everyone for what is potentially coming,” Malcolm Freeman, a director at broker Kingdom Futures, said in a note. Higher interest rates could reduce money supply and potentially prompt investors to pull back from riskier assets such as metals. Meanwhile, the Yangshan copper premium SMM-CUYP-CN was last at $28 a tonne, hovering around its lowest since February 2016 and down 75% compared with May 2020, indicating weakening demand for imported metal in China. FUNDAMENTALS * LME nickel fell 0.3% to $17,840 a tonne, aluminium slipped 0.1% to $2,424 a tonne, zinc advanced 0.3% to $3,007 a tonne, and tin gained 0.5% to $30,680 a tonne, not far off the decade-high of $31,135 struck a week ago. * On the ShFE, aluminium closed down 1.1% at 18,260 yuan a tonne, nickel shed 1.2% to 130,080 yuan a tonne, while lead ended 0.4% higher at 15,050 yuan a tonne. * LME cash aluminium was at a $5.24 a tonne discount to the three-month contract CMAL0-3, the smallest discount since May 7, indicating nearby supplies are tightening. * For the top stories in metals and other news, click or $1 = 6.3911 Chinese yuan Reporting by Mai Nguyen; additional reporting by Tom Daly; Editing by Ramakrishnan M. and Sherry Jacob-Phillips Our Standards: The Thomson Reuters Trust Principles.