* Europe will provide a severe test for coalition
* Could Deputy Prime Minister Clegg be ousted?
* A chance for Labour to pull further ahead in polls
LONDON, Dec 30 (Reuters) - British Prime Minister David Cameron's "odd-couple" coalition government will come under increased strain in 2013, newspapers predicted, with the divisive issue of Europe aggravating tenisons between them as the feelgood factor of the Olympic Games and the Queen's Diamond Jubilee fades.
Two key moments will be Cameron's long-awaited speech on Britain's relations with the European Union, expected in the next few weeks, and local government elections in May which could prompt a revolt against Liberal Democrat Deputy Prime Minister Nick Clegg.
Also expected to weigh on coalition sentiment in 2013 will be the improved standing of Labour opposition leader Ed Miliband and the rise of the anti-EU UK Independence Party (UKIP).
"It has always been tricky for Cameron and Clegg to present themselves as united," said The Observer. "This tension will become more acute in the 12 months ahead."
Unable to win an outright victory in the 2010 general election, Cameron's centre-right Conservatives persuaded the much smaller, left-leaning Liberal Democrats to join them in coalition to help solve Britain's economic problems.
The unequal electoral strength of the two parties and the ideological gulf between them have long encouraged Britain's newspapers to speculate whether they will be able to last together until the next election in 2015.
Nowhere is the divide more marked than over Europe, with the Conservatives increasingly divided on the EU as the euro zone's economic problems have worsened and the LibDems staunch in their support for Britain's EU membership.
"The coalition has proved far stronger than many wiseacres had assumed and the two parties have agreed to differ in ways in which some had thought impossible - but Europe may prove a bridge too far," said the Sunday Times.
The Sunday Telegraph warned: "The centre of gravity in the Conservative Party is shifting unambiguously towards a much steelier collective position on Europe.
"The question in 2013 is whether Cameron can keep pace with his party on Europe...and still hold together his governing partnership with the most Europhile party in the U.K."
A defining moment, the papers agree, will be Cameron's long-awaited speech in which he is expected to give details of how he sees Britain's future relationship with Brussels. No date for the speech has yet been announced.
The rise of UKIP, which has been beating the LibDems in by-elections this year, has sharpened the debate on Europe by offering a potential alternative to anti-EU Conservative voters.
In November, for example, UKIP came second to Labour in the safe northern Labour seat of Rotherham while the LibDems could only manage eighth place.
Clegg's standing among LibDem voters has plunged due to the compromises he has had to make in coalition - notably on the controversial tripling of higher education tuition fees - and several observers predict he may face a leadership challenge if May's local government elections prove a disaster for the party.
"If the May results are as bad as expected, his party will weigh up whether continuing with the service of the deputy prime minister spells near certain obliteration," wrote the Sunday Times.
"A change at the top need not, of itself, destroy the coalition but would, at the very least, change it beyond recognition," it added.
Among those who might replace Clegg, several pundits have said, is former energy minister Chris Huhne if he wins a criminal case being brought against him next year for allegedly perverting the course of justice.
The prospect of a squabbling government and more economic pain being heaped on voters as austerity measures cut even deeper in 2013 could offer a real opportunity for Labour leader Ed Miliband to increase his lead in the opinion polls, the papers say.
"This time last year, Labour's leader was still regarded as a lightweight, but a showy party conference speech and some steady (parliamentary) performances have changed that," the Sunday Times said.
But most commentators agreed Miliband needs to put more flesh on the bones of Labour's policies in 2013.
"What is missing is the picture inside," said The Observer. "It may be far too early for Labour to be trying to write a detailed manifesto for an election...but in 2013 his rebooted policy review will have to start producing some concrete results."
Contrasts abound between the glowing Olympic memories of the past Summer and the relentless austerity to come.
"These memories have substance and will serve us well in the bleak times ahead," wrote the Sunday Telegraph. "But memories are what they are and will be. What's left will be jagged, arduous and demanding."