May 16 (Reuters) - Copper and other industrial metals inched higher on Monday, as hopes of a revival in demand grew after China set out plans to ease COVID-19 restrictions, although shockingly weak industrial output data from world's second-largest economy limited gains.

Benchmark three-month copper on the London Metal Exchange (LME) was up 0.4% at $9,193.50 a tonne, as of 0436 GMT.

The most-active June copper contract on the Shanghai Futures Exchange rose 0.9% to 71,220 yuan ($10,486.95) a tonne by the midday break.

LME aluminium climbed 1.6% to $2,833.50 a tonne, zinc gained 1.2% to $3,531.50, lead was up 0.6% at $2,091 and tin rose 1.5% to $33,875.

"If China does loosen lockdowns even a smidgen, it opens the door to policy easing," said Stephen Innes, managing partner at SPI Asset Management.

"The horrible miss in China's industrial output could be a rude wake-up call to mainland policymakers to open things up more within the context of zero-COVID policy."

Shanghai set out plans on Monday for the return of more normal life from June 1 and the end of a painful COVID-19 lockdown that has lasted more than six weeks and contributed to a sharp slowdown in China's economic activity.

DATA: China's economic activity cooled sharply in April as widening lockdowns took a heavy toll on consumption, industrial production and employment. Data showed China's industrial output fell 2.9% in April from a year earlier.

SUPPORT: Chinese financial authorities on Sunday allowed a further cut in mortgage loan interest rates for some home buyers, in another push to prop up its property market.

DOLLAR: The dollar held steady near a 20-year high against its rivals, as investors sought safety due to fears of a slowdown in global economic growth.

CHILE: A constitutional assembly in the world's top copper producing nation on Saturday rejected a major overhaul to mining rights, including expanding Chilean state ownership.

PRICES: Shanghai aluminium gained 2.5%, zinc was up 0.6%, nickel slipped 1%, lead eased 0.3% and tin climbed 1%. ($1 = 6.7913 Chinese yuan) (Reporting by Brijesh Patel in Bengaluru; Editing by Subhranshu Sahu)