Dec 6 (Reuters) - Copper prices in London edged up on Tuesday on demand hopes in top consumer China after more cities eased COVID-19 restrictions, but a firm dollar capped gains.

Three-month copper on the London Metal Exchange was up 0.1% at $8,395 a tonne by 0730 GMT, while the most-traded January copper contract on the Shanghai Futures Exchange edged down 0.7% to 65,770 yuan ($9,402.43) a tonne.

China's capital Beijing dropped the need for people to show negative COVID tests to enter supermarkets and offices, the latest in an easing of curbs across the country following last month's historic protests.

The country may announce 10 new COVID-easing measures as early as Wednesday, sources said, supplementing the 20 unveiled in November that set off a wave of relaxations nationwide.

Easing restrictions are supportive to copper prices, said ANZ analysts in a note.

"The market has shrugged off signs of weakness in the physical market," they added.

Yangshan copper premium fell to its lowest since July 22 at $72.50 a tonne on Monday, indicating weakening demand for imported copper into China.

Withdrawals of copper inventories have also been slowing across the LME, SHFE and Chinese bonded warehouses. SHFE copper inventories were at 65,226 tonnes on Friday, more than double the level seen at the end of September.

A steady dollar, which makes greenback-priced commodities expensive to holders of other currencies, also capped the gains in metals prices.

LME aluminium fell 0.7% to $2,504.50 a tonne, zinc eased 0.2% to $3,121 a tonne, lead was down 0.9% at $2,219 a tonne and tin dropped 0.6% to $24,295 a tonne.

SHFE nickel rose 0.9% to 206,700 yuan a tonne, tin jumped 2.4% to 195,010 yuan a tonne, lead was steady at 15,940 yuan a tonne and aluminium fell 0.4% to 19,185 yuan a tonne.

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($1 = 6.9950 yuan) (Reporting by Mai Nguyen in Hanoi; Editing by Subhranshu Sahu)