By Matt Falloon

LONDON, Oct 1 (Reuters) - Britain's Conservatives slippedbehind Labour in an opinion poll this week for the first time inthree years, even before the centre-right party's coalitiongovernment details its spending cuts in October.

Ousted in May after 13 years in power, Labour has selected anew leader, avoided the post-election implosion predicted bysome and looks primed to attack the coalition as it implementsits severe austerity drive.

The Conservative-Liberal Democrat administration is facingthe first real test of its durability as ministers grapple overwhere the axe will fall to cut a record budget deficit.

A few government departments have already agreed theirfunding for the next four years but full details of the spendingreview will not be available until Oct. 20.

An emergency budget in June -- with its tough austerity plan-- calmed investor nerves over soaring government borrowing butthere is a growing risk that Britain's robust recovery from an18-month recession is about to run out of steam.

The strength of the coalition partnership -- an unusualmarriage of convenience in British politics -- has facedincreasing scrutiny because the ratings of the left-leaning LibDems have collapsed since the May 6 election.

Below are the key political risks to watch.

THE COALITION AND THE DEFICIT

Markets, credit ratings agencies and the IMF have warmed tothe planned tax hikes and steep spending cuts aimed at slashinga budget deficit running close to 11 percent of national output.

But agreeing on and executing spending cuts will test thecoalition and there is no guarantee that the administration --the first partnership government since World War Two -- willlast until the next poll, due in 2015, to see the cuts through.

The risk of a swift collapse is very slim but signs thecoalition is struggling to deliver could put pressure onsterling and trigger a rise in currently low gilt yields.

Worse could come if the global economy heads into anotherslowdown, as many now fear. Slower than expected growth willspoil the coalition's plan to all but eliminate the deficit by2015 and raise questions about the wisdom of their approach.

One Bank of England policymaker has warned Britain risksgoing into the kind of prolonged economic slump Japan sufferedin the 1990s unless more action is taken to boost growth.

What to watch:

-- Indications of stable government for at least a couple ofyears to allow the coalition to get on with cutting the deficit.

-- Economic data from across the world. The worse theoutlook gets, the harder it will get to implement cuts at home.

THE LABOUR PARTY

Labour crashed out of government this year after rulingsince 1997, leading commentators to argue the centre-left partywas destined for a long spell in the political wilderness.

Former Prime Minister Gordon Brown stepped down in theaftermath and the party elected a new leader -- 40-year-oldformer energy minister Ed Miliband.

Labour has nudged in front of the Conservatives in polls andcould now prove a real thorn in the side of the coalition.Labour are specifically keen on targeting disaffected Lib Demsto weaken the coalition's resolve.

What to watch:

-- How quickly Labour galvanises behind its new leader.

-- How successful the party is at exploiting any cracks inthe ruling coalition.

VOTING REFORM

Voting reform could prove critical to coalition survival.

The Conservatives don't want to change Britain'sfirst-past-the-post voting system but it is a matter of urgencyfor the Lib Dems, whose parliamentary seat count does notreflect the party's performance in the popular vote.

Agreeing to hold a referendum next year was a deal-clincherfor the Lib Dems in coalition talks, but has stirred updiscontent among Conservative parliamentary backbenchers.

If the Lib Dems fail in their bid to bring in an AlternativeVote system, the party's grassroots supporters may start towonder if life in a coalition government is really worth it.

If they succeed, Cameron may come under pressure from withinhis own Conservative party.

What to watch:

-- How the public reacts to different messages from thecoalition on voting reform. How bitter the campaigning gets,potentially opening up cracks in the partnership.

THE BANKS

The Bank of England will take over macroprudentialregulation of the banks by 2012, with sovereign debt concernsand a continued dearth of credit likely to weigh on thefinancial sector for the foreseeable future.

The coalition has announced a 0.07 percent bank levy onbalance sheets, without complete international approval. The taxis expected to raise 2.5 billion pounds ($3.95 billion) annually-- far less than had been speculated earlier this year.

But Lib Dem business secretary Vince Cable has warned banksfurther taxes could be on their way if they don't curtailbonuses and dividends and fail to boost lending to business.

What to watch:

-- A report on splitting banks is expected within a year.Any swift changes to banks' structures are likely to hurt sharesin banks such as Barclays and HSBC.

EXTERNAL AND INTERNAL STRAINS

Cameron wants British combat troops out of Afghanistanwithin five years and an Afghan army in place that can take careof security.

Analysts are sceptical that this can be achieved, given theongoing security problems on the ground. With the war growingincreasingly unpopular at home, the government must deliver onits aim or risk losing support among middle ground voters.

The coalition might also face an upsurge in republicanviolence in Northern Ireland and some form of social unrest inBritain is almost inevitable as unionised workers in the publicsector protest against big spending cuts.

Relations with the European Union will also test thecoalition's mettle. The Conservatives are generally euroscepticwhile the Lib Dems are committed fans of the European project.

What to watch:

-- Any worsening in relations with the EU could imperil LibDem support for the coalition.

-- How the unions react to public spending cuts. (Editing by Sonya Hepinstall)