Unpicking a relationship that has grown over more than 40 years was never going to be easy. But once the result of June’s Brexit referendum had sunk in, the full import of the task of separating Britain from the EU began to become apparent.

Bedevilling the situation was the reality that the Leave campaign — many of whom appeared to have not expected to win — harboured many and varied ideas about the kind of post-Brexit UK they wanted to see, some of which seemed at a distinct tangent to reality. And, while the result of the referendum indicated a general desire to leave, the various models for a new relationship were not on the ballot paper.

In this context, the contours of a new agreement between the UK and the EU are extraordinarily uncertain. They range from continued membership of the EU, perhaps if a future second referendum rejects whatever deal is negotiated, to a position completely outside the union, trading on the basic terms available to any member of the World Trade Organisation.

Perhaps the most important variable around which all this turns is the free movement of workers. It was one of the key campaigning issues for the Leave side and Theresa May, the prime minister, has repeatedly said that some limit on immigration is a non-negotiable outcome.

If that is the case, it rules out a number of options that would keep Britain relatively close to the EU. It would be impossible to conclude a Norway-style deal where the UK, as a member of the European Economic Area, remained a full member of the single market. Nor would it be possible to retain access to the single market via a Swiss-type framework, which achieves a similar outcome through a series of standalone arrangements.

This creates a particular difficulty for the UK, whose exports are unusually concentrated in the service sector. Since the cross-border supply of services frequently involves workers having to move back and forth — few management consultants will do large jobs without site visits — European officials are fond of saying that free movement of workers is indivisible from the single market.

Special Report Britain after Brexit © Getty How will the future look for the City, entrepreneurs, farmers, industry and from a political perspective?

Meanwhile, the apparent alternative, a bilateral UK trade agreement with the EU, is highly unlikely to give the UK much access to the European services market, judging by the content of deals such as the EU-Canada pact currently awaiting ratification. As an added complication, it is not yet clear whether the UK will be seeking bilateral trade deals with other countries. If it stays within the EU customs union and accepts a common external tariff, Britain’s ability to sign pacts with third parties will be more or less non-existent.

UK ministers will probably try to negotiate some kind of deal whereby the UK gets as much access as possible to the single market while maintaining enough control over free movement to appease the British public.

As an example of such a halfway house, a group of academics and experts have published a paper for Bruegel, the European think-tank, proposing a “continental partnership”. Britain would join an “outer circle” around the core EU, a circle that could possibly expand to include Switzerland, Iceland, Norway and, in the longer run, Ukraine and Turkey.

Countries such as France do not want to start a stampede of member states out of the inner core and into the outer

The study envisages an intergovernmental deal that maintains as much as possible of the function of an integrated market, including tariff-free access, common rules or standards, a single competitiveness and state aid regime and a contribution to the EU budget. But it would place the UK outside what it calls the “economic-political constitution” of the single market, which guarantees, among other things, full freedom of movement for labour. The UK and other continental partnership countries would be consulted on EU legislation and be able to propose amendments, but not vote on it.

The proposal has the advantage of flexibility, allowing the UK and EU to choose areas of co-operation and binding Britain to common decisions. But such a deal would almost certainly face tough opposition from some EU member states and from the European Commission and Parliament. Countries such as France, faced with their own strong eurosceptic and anti-immigration parties, do not want to start a stampede of member states out of the inner core and into the outer. Though the Commission is by no means the force it once was, it too will weigh in heavily on the side of the UK being either fully in or fully out.

For the moment, a cacophony of confusing briefings and counter-briefings — and a suspicion that some ministers simply do not know what they are talking about — means that the UK’s post-Brexit form is a riddle wrapped in a mystery inside an enigma. Only when Mrs May’s government decides what it wants and the rest of the EU has had a chance to digest it will the boundaries of the possible become clear.