* FTSEurofirst 300 gains 1.1 percent, up for 3rd day
* Investors bet on passage of Greek austerity plan
* Miners, banks among top gainers; Greek banks surge
LONDON, June 29 (Reuters) - European shares gained for a third straight day on Wednesday as investors bet Greece's parliament will pass a crucial austerity plan demanded by international lenders as a condition for providing more funds to prevent a default.
But equity prices are unlikely to break their recent trading range even if there is a positive Greek vote. Investors are already looking ahead to the difficulties Greece will face in implementing the unpopular austerity plans and also to the end of the second round of quantitative easing in the United States, analysts said.
Market activity was dominated by short-term players, while large funds broadly stayed on the sidelines, watching the developments. Fund managers said they needed to see more clarity before investing heavily in equities and that might not happen before the end of the summer.
At 0851 GMT, the FTSEurofirst 300 index of top European shares was up 1.1 percent at 1,092.69 points after rising 0.6 percent in the previous session.
Greek banks jumped 4.9 percent, the European banking index rose 1.6 percent, while Greek shares rose 2.5 percent on hopes of a positive vote. The Thomson Reuters Peripheral Eurozone Banks index gained 2.4 percent, but is down 15 percent from a two-month ago level.
"A lot of work has been done behind the scenes to ensure that the proposals get passed, and that optimism is getting reflected into the share prices," said Graham Bishop, equity strategist at RBS.
"The passage of the austerity plan will certainly help, but that's not to say there are not any more hurdles. The next hurdle will be the implementation of the measures and the government will be closely watched on that."
The vote on Greece's five-year austerity plan, due later on Wednesday, has provoked violent demonstrations in the country, The plan is needed to secure a new tranche of EU/IMF funds to prevent Greece becoming the first developed nation in more than 60 years to default on its debts.
Late on Tuesday, the government of Prime Minister George Papandreou received a boost when one of three rebel deputies from his ruling PASOK party backtracked on his previous opposition and said he would vote for the package that includes spending cuts, tax increases and privatisations.
Miners were also in demand as key metals prices advanced. The European basic resources index was up 1.8 percent, while Antofagasta rose 4 percent.
RISK APPETITE RISES
The Euro STOXX 50 volatility index , one of Europe's main barometers of sentiment, fell 5 percent, indicating a rise in appetite for riskier assets such as equities. But the index has jumped about 45 percent in the past two months, signalling persistent investor jitters.
"For the market participants worldwide, there are two bigger issues which are potentially going to drive company profits much more than the Greek issue," said Lothar Mentel, chief investment officer at Octopus Investments.
He said investors would continue to focus on any weakness in emerging economies and on the impact of the second round of quantitative easing. A positive result of the Greek vote could send Britain's FTSE 100 higher, but the index was unlikely to break the 5,900 level in the near term, he added.
Mentel, whose fund company manages 2.5 billion sterling ($4 billion), said shares could fall 2 to 3 percent if there was negative news on the Greek vote.
The FTSE 100 index was up 1.1 percent at 5,829.85 points, while Germany's DAX rose 1.2 percent and France's CAC 40 was up 1 percent.
Among individual movers, Italian luxury shoemaker Salvatore Ferragamo rose 8.6 percent on their first day of trading, defying expectations for a muted debut.
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