* Britain's main opposition Labour Party supports rivals in EU vote
* Labour scores victory over Cameron, but accused of hypocrisy
* Britain's role in Europe dominates UK political debate once again
LONDON, Nov 1 (Reuters) - Giving Prime Minister David Cameron a bloody nose over Europe may have given Britain's opposition Labour Party a short-term glow, but their lurch towards the anti-Brussels camp risks leaving them divided, isolated and lacking credibility.
After years of broadly pro-European policies, the centre-left party joined a rebellion organised by members of Cameron's Conservatives demanding he pushes for a real-terms cut in the European Union budget at talks this month.
Cameron, who supports a rise in line with inflation, lost the non-binding but politically embarrassing vote in parliament late on Wednesday.
Only two days before, former Labour prime minister Tony Blair issued a warning that playing "short-term politics" on Europe could leave Britain out in the cold when it should be playing a bigger role in shaping EU reforms.
Labour's prize was a barrage of Halloween-inspired headlines talking of Europe coming back to haunt Cameron in a "Nightmare on Downing Street", a reference to his official residence.
That piled pressure on Cameron, chasing Labour in the polls before a 2015 election and trying to regroup after a bruising period that saw a senior minister quit and repeated accusations of elitism and incompetence.
"The short-term advantage is that they have embarrassed the government," said John Curtice, politics professor at Strathclyde University in Scotland. "The long-run question is whether Labour are playing with fire."
The euro zone crisis has driven British politicians on all sides to demand big EU reforms. Debate over a referendum on Britain reworking its role in the 27-member bloc or even leaving after nearly 40 years has climbed to the top of the agenda.
Talking down Europe plays well with the big chunk of the British electorate that wants to leave the European Union, an institution often portrayed in the UK media as a wasteful, interfering and powerful bureaucracy.
A YouGov survey in October found 49 percent of those polled would vote to leave the European Union if they were given a say in a referendum, against 28 percent who would vote to remain in.
However, Labour's shift could widen divisions between the party's pro-Europeans and those who are less keen. It also left Labour open to charges of making a tactical misstep for backing a vote that is doomed to failure and which could send the wrong signal to allies in Europe.
"I'm not sure who's the bigger loser," political commentator Michael White wrote in the left-leaning Guardian newspaper. "My hunch is that the short-term satisfaction the Labour leader gets from helping to humiliate the prime minister will be outweighed in the long-term by the charge of shabby opportunism which fails to impress voters."
Cameron accused Labour leader Ed Miliband of "rank opportunism", while one Labour politician, Margaret Hodge, was reportedly overheard in parliament calling the vote "hateful".
Deputy Prime Minister Nick Clegg, leader of the Liberal Democrats, the junior coalition partner, said Labour's "change of heart is dishonest...hypocritical".
Conservatives pointed out that Labour wants real-terms cuts in EU spending while criticising the British coalition for reducing public spending. The government also highlighted Labour's support for EU budget rises and a cut to Britain's annual budget rebate when it was in power.
The centre-right Conservatives are known for historic divisions on Europe that helped bring down Margaret Thatcher and undermined John Major, both former prime ministers.
But Labour also has its share of tribalism on the topic, one of the most intractable in British politics. Senior figures on the party's left campaigned against Britain's membership of the EU's forerunner in the early 1970s and debate over its role in Europe raged into the Blair and Gordon Brown years of 1997 to 2010.
Labour foreign affairs spokesman Douglas Alexander played down talk of a U-turn on Europe, saying they had been calling for EU budget cuts since July.
"It is a losing argument for pro-Europeans to somehow suggest that Europe should be exempted from the economic challenges that many countries are facing," he said.