David Cameron will need patience, guile and luck to tackle Britain's relationship with Europe

Of all the challenges facing David Cameron by far the most pressing and most intractable is renegotiating Britain’s relationship with the European Union.

The Prime Minister must pull off the trickiest of balancing acts: he must negotiate a new deal for Britain that is acceptable to 28 other European leaders; he must then unite his increasingly anti-European party behind it before finally successfully putting the proposals to the public in a referendum.

A week may be a long time in politics – but two years seems like a very short time to resolve one of the most intractable and fractious political issues of the last quarter of a century.

That said, despite the problems and the narrowness of Cameron’s majority, there is some cause for optimism that a workable deal is achievable. But it will take patience, guile and a fair amount of luck.

The main sticking point is how to tackle the politically toxic issue of migrant workers and their right to claim benefits in Britain.

In a speech last November Mr Cameron made clear that any new deal would have to give the UK power to restrict both in work and out-of-work benefits to EU migrants who have been in the UK for less than four years.

Eastern European leaders have rejected this demand out of hand describing such benefits as “sacrosanct”. “They cannot be touched,” Peter Javorcik, Slovakia’s Europe Minister, told the Financial Times.

But this position is unlikely to hold. While eastern European countries might be opposed to the British proposals the prospect of the UK leaving the EU altogether would act as a strong incentive for them to compromise.

“They may not like it but if the alternative is that Britain leaves the EU (and freedom of movement is lost altogether) then agreeing to these limited restrictions may seem like a small price to pay,” said Mat Persson, director of the influential think-tank Open Europe. “I think there is scope for compromise.”

Mr Persson added there was also a misconception in other European capitals about the nature of what Mr Cameron was trying to achieve on benefits which, if resolved, could make compromise easier.

“Most other European countries have a contributory system of benefits which automatically exclude migrant workers from claiming benefits until they have worked in the country for a certain period of time,” he said. “That is not true of the UK where benefits are universal.”

This, Mr Persson said, was a particular problem with tax credits – which were designed to incentivise British people to come off benefits and get a job but are actually being disproportionately claimed by EU migrants.

“The UK system is not well understood in other European countries. When it is explained I think most countries will see giving Britain some flexibility is acceptable as long as the principle of free movement of people remains.”

Another big sticking point is Mr Cameron’s call for the changes he negotiates to be enshrined in EU treaties. There is no absolutely no appetite for this among in other European capitals – especially as many countries would have to endorse treaty change with referendums.

But again, compromise is possible. After the Danes rejected the Maastricht Treaty in a referendum a solution was found by adding “protocols” to the treaty to mollify the Danes while keeping the basic framework of the agreement intact.

A similar devise could be used again: In areas of dispute such as Britain’s participation in the Working Time Directive a protocol could be added to the treaty giving the UK an opt out – and the protocol would then be incorporated into EU law the next time the treaties were formally revised.

“A lot of things could be resolved by protocols,” said Mr Persson. “In the EU politics tends to trump law and there are ways get stuff done outside of formal treaty change.”

But a German Government source said much would depend on the attitude that the British took to the renegotiation. They added that in order to be successful the UK would need to build support across all 28 countries and not rely on the Franco-German access to force things through.

“They’ll have to do it the ‘European way’ by building support among all member states at a lower level before the negotiations ever reach Brussels,” they said.

“These are matters which will be decided by one-member-one-vote. It is not enough for Britain just to talk to Berlin and Paris and expect everyone else to fall in line. That is not the way things work any longer.”

But getting a deal is only the first part of Mr Cameron’s difficulties. He then has to sell that deal to his own party – before taking it to the country and winning a referendum.

Even Cabinet ministers such as Philip Hammond and Michael Gove are now among those who, in certain circumstances, would favour pulling out of the EU – while for others in his parliamentary party no deal would be a good enough deal to stay in.

Downing Street is gambling though, that in the event of a reasonable deal being negotiated, they will be able to hold the line – especially with an improving economy that is likely to reduce the toxicity of immigration as a political issue.

If the worse comes to the worse, they say, Mr Cameron could allow Tory MPs a free vote on the issue and divide on the referendum for the sake of long-term party unity.

Many uncertainties and imponderables remain and the final result is far from clear. One thing is certain though – the European question will dominate political debate in which it has not done since early the 1990s and the outcome will define Mr Cameron’s legacy as Prime Minister.

Scenario One

Cameron succeeds in persuading all 28 leaders to back a package of EU reform. Calls for a “yes” vote in the referendum and wins.

Scenario Two

Cameron succeeds in persuading all 28 leaders to back a package of EU reform. But despite calling for a “yes” vote he fails to win and is forced to resign.

Scenario Three

Cameron fails to get agreement on a package of EU reforms in Brussels. Recommends a “no” vote in the referendum and wins, resulting in Britain leaving the EU.

Scenario Four

Cameron fails to get agreement on EU reforms. Recommends a “no”, vote and buts loses. Britain stays in the EU and Cameron resigns.