Oct 5 (Reuters) - Benchmark London copper prices slipped in choppy trade on Wednesday as the U.S. dollar steadied following big losses the day before, while speculation that top metal consumer China may soon ease its zero-COVID policy lent some support.

Three-month copper on the London Metal Exchange was down 0.2% at $7,700 a tonne, as of 0435 GMT.

The dollar steadied on Wednesday after a sharp rate rise in New Zealand poured cold water over hopes for a pause or slowdown in the U.S. Federal Reserve's intentions for aggressive hikes.

The dollar's weakness, which makes greenback-priced metals cheaper for holders of other currencies, had helped lift copper prices to their highest in more than a week on Tuesday.

"Tighter monetary policy has been a strong headwind for base metals, with concerns demand will falter amid higher borrowing costs," said ANZ senior commodity strategist Daniel Hynes.

Copper's pullback also followed news that supervisors at Antofagasta Minerals' Los Pelambres copper mine in Chile expect to reach a new contract agreement in a mandatory mediation process with the company, which is set to begin later this week to avoid a strike at the site.

Growing speculation that Beijing may soon start relaxing its zero-COVID strategy, however, provided some support to copper, Hynes said.

"Even a partial relaxation would be welcome news for the sector (as) demand has been crippled by the ongoing lockdowns across the country," he said.

Base metals trading remained subdued though with the Shanghai Futures Exchange closed until Oct. 7 for China's Golden Week holidays.

Lead was up 0.7% at $1,950.50 a tonne, aluminium gained 0.1% to $2,349.50, while zinc shed 0.2% to $3,040.

For the top stories in metals and other news, click or (Reporting by Enrico Dela Cruz in Manila; Editing by Sherry Jacob-Phillips)