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* FTSEurofirst 300 down 1 pct; off 2.7 pct on week
* Dividend worries knock KPN shares
* Melrose tumbles on weak outlook
By Tricia Wright
LONDON, Nov 16 (Reuters) - European shares sank to a 3-1/2-month closing low on Friday and chalked up their worst week since the end of May on persistent concerns over U.S. fiscal policy and the euro zone debt crisis.
The FTSEurofirst 300 ended down 1 percent at 1,067.45, its lowest close since Aug. 2, taking its weekly loss to 2.7 percent.
"Investors are pretty cautious and uncertain. It's been a difficult week," said Michael Hewson, senior markets analyst at CMC Markets.
"You've got a growing acceptance that there will be no quick resolution either in the U.S. or in Europe and ... what people are starting to do is take a bit of money off the table for the year, because further upside is likely to be very limited."
Investors were focused on the economic outlook for the United States, where politicians struggled on in their bid to avert the 'fiscal cliff' of $600 billion in tax hikes and spending cuts that could jeopardise growth.
Data on Friday showing an unexpected fall in U.S. industrial output in October threw the problems facing the world's biggest economy into sharp relief.
"We've hardly been talking to anyone about what's going on in Europe. Everyone's worried about America, and I think it's going to continue," said Will Hedden, a trader at IG in London.
Still, uncertainty over the next steps with regard to Greece's finances also weighed on sentiment, with banking shares in the euro zone the worst hit, down 2.7 percent and giving back yet more of their recent three-month rally.
Against a gloomy macro backdrop, with data released this week showing the euro zone is already back in recession, investors faced up to potential cuts to dividend payouts and fretted about corporate outlooks.
Dutch telecoms group KPN tumbled 7.1 percent, in brisk volume, on concern over the sustainability of its dividend.
Trading volume in KPN stood at more than three times its 90-day daily average, against the FTSEurofirst 300 on 115 percent of its 90-day daily average.
And British engineering group Melrose, which said the sales outlook for 2013 has become uncertain, was left nursing an 11.5 percent drop in its share price.
"I don't think any sector is feeling terribly confident about the future," said Frances Hudson, global thematic strategist at Standard Life Investments, which has around 158 billion pounds ($250 billion) of assets under management.
"We're going into the festive season with households wondering how they're going to pay for it, which isn't a strong underpinning for consumption. And of course consumption is such a big part of most developed economies."