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METALS-Copper, lead and zinc hit near three-month highs

* LME/ShFE arb - http://tmsnrt.rs/2oQ5nm2 (Adds official midday prices)

LONDON, June 28 (Reuters) - Copper, lead and zinc prices hit near three-month highs on Wednesday boosted by sharp falls in the dollar, signs of tighter supply and optimism over Chinese demand, although worries about U.S. economic growth capped the upside.

The U.S. dollar touched its lowest level against the euro in a year on Wednesday after hawkish comments from the head of the Bank of England fueled bets on tighter monetary policy in Europe.

A weak dollar makes dollar-priced metals cheaper for holders of other currencies.

In the United States, concerns persisted about poor economic readings and doubts over President Donald Trump's ability to push through tax cuts and spending increases.

Still, metals were still bid thanks to signs that supply is shrinking as exchange inventories fall and amid indications of solid demand in China, the world's largest metals consumer.

"As we head into summer, we expect more capacity reductions in China to meet environmental restrictions, and we think consumers are buying stock ahead of that," said SP Angel analyst John Meyer.

"The market got ahead of itself in the first quarter with (hopes for) Trump's infrastructure plans, that's not happening now but, against that, China growth is ok."

* COPPER PRICE: London Metal Exchange copper ended up 0.4 percent at $5,881 a tonne, having struck its highest since early April at $5,881.50.

* COPPER STOCKS: LME data showed headline copper stocks <MCU-STOCKS> down to 248,675 tonnes, having slid 30 percent since early May, and on-warrant or available stock levels have shed 40 percent over the period.

* LEAD & ZINC: Zinc ended down 0.5 percent at $2,734 a tonne, having hit its highest since early April at $2,764, while lead closed up 0.4 percent at $2,296, having reached its strongest since early April at $2,302.

* TECHNICALS: Cash zinc traded at a premium of $0.50 a tonne to the three-month price <CMZN0-3>, a high since early May and indicating tight nearby supply. Cash lead traded at a discount of just $13.01 to the three month price <CMPB0-3>, near its narrowest since mid-May.

* CHINA POLLUTION: China on Tuesday appointed a new environment minister who has promised a "protracted battle" to clean up the nation's notoriously polluted air, water and soil.

* OTHER METALS: Aluminium ended up 0.7 percent at $1,896 a tonne, nickel closed up 0.1 percent at $9,270 while tin ended up 0.9 percent at $19,445.

($1 = 6.7999 Chinese yuan renminbi)

(Additional reporting by Melanie Burton; Editing by David Evans and Edmund Blair)