(Reuters) - Hong Kong residents voted for a new legislature on Sunday, a day after the territory's Beijing-backed leader backed down on a plan to introduce a compulsory Chinese school curriculum after tens of thousands of people took to the streets.

Some 3.4 million of the city's seven million people are eligible to directly elect just over half the seats in the 70-seat legislative council at a time when anger over perceived Chinese influence in the former British colony is growing.

On Saturday, Hong Kong's pro-China chief executive Leung Chun-ying withdrew the plan for compulsory patriotism classes that protesters described as Chinese Communist Party-style propaganda aimed at indoctrinating children.

"It will, at least, contain the damage, and I'm sure it will relieve the pressure on the pro-establishment and the pro-Beijing candidates," said political scientist Joseph Wong.

Hong Kong is a freewheeling capitalist hub which enjoys a high degree of autonomy, but Beijing has resisted public pressure for full democracy and has maintained a high degree of influence in political, media and academic spheres.

Sunday's polls are a rough barometer of public support for Leung and his pro-Beijing allies on the one hand, and the opposition pro-democracy camp on the other, which is seeking to maintain its one third majority to give it veto power over policies.

A host of China-linked controversies have dealt a blow to Leung and may help bolster the pro-democracy parties at the ballots, analysts say, making it more difficult for his administration to enact policies in a fractious legislative council.

"I see many more voters this time round. Usually the mornings are quieter," said one voter surnamed Hon as ballot centres opened across Hong Kong on a sunny Sunday morning.

"Before it didn't matter so much who got in. but this time, I thought it was important to vote to stop people and parties I didn't want from getting into the legislature," said another voter surnmaed Chan.

In 2003, a demonstration by half a million people against Hong Kong's first China-backed leader, Tung Chee-hwa, led to the scrapping of a controversial anti-subversion bill and his resignation midway into his second five-year term in 2005.

While tensions have grown over mass Chinese tourism, an influx of mainland mothers giving birth in the city and the national education plan, others said livelihood issues were crucial.

"I vote for people who can help us the most," said Anthony Tsang, a deliveryman voting at a rural polling station in a sleepy offshore island. "I care about livelihood, (high) housing costs, wages and medical care."

Over a frenetic past week, the administration has scrambled to quell some of the anger by providing more affordable housing and mitigating the impact of mass China tourism.

(Additional reporting by Tan Ee Lyn and James Pomfret; Editing by James Pomfret and Sanjeev Miglani)

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