BEIJING, July 10 (Reuters) - London copper gave up early gains to trade lower on Tuesday, while zinc slumped to its lowest in more than a year, as a metals rally driven by investors looking for bargains after a trade war-fuelled sell-off appeared to run out of steam. The United States on Friday slapped tariffs on $34 billion of goods from top metals consumer China, which responded in kind. Fears that the trade spat could dampen demand for industrial metals had weighed on prices. Zinc was one of the worst hit metals, falling by 4.2 percent in London and above 5.3 percent in Shanghai last week, with the declines continuing on Tuesday. "A lot of zinc concentrate is coming on line from mines across the world," this year, said Helen Lau, an analyst at Argonaut Securities in Hong Kong, adding that demand for zinc in steel galvanising in China was seeing "a bit of a slowdown." FUNDAMENTALS * ZINC: Three-month zinc on the London Metal Exchange sank as much as 2.8 percent to $2,630.50 a tonne, its lowest since June 22, 2017. Shanghai zinc closed down 2.2 percent at 21,755 yuan ($3,289.58) a tonne. * LME COPPER: London Metal Exchange copper slipped 0.7 percent to $6,348 a tonne, as of 0742 GMT, following a 1.7-percent gain from the previous session. The metal lost more than 5 percent last week. * SHFE COPPER: The most-traded September copper contract on the Shanghai Futures Exchange closed up 0.4 percent at 49,760 yuan a tonne. * RUSAL: United Company Rusal, the world's second-biggest aluminium producer, in May increased aluminium exports to 197,000 tonnes, up almost threefold from April, Interfax news agency reported. * BLOCKCHAIN: Online metal concentrates exchange Open Mineral is seeking to build a consortium of mining companies and financial institutions to create a blockchain system for minerals trading and logistics.