‘Brexit means Brexit’ is one of the most brilliant political soundbites of recent times. It worked wonders for Theresa May during the Tory leadership contest. It showed that she didn’t intend to ignore the referendum result — that would have been politically suicidal — but the phrase is essentially meaningless. Brexit could mean many things.

The question of what it actually is will define British politics for the next five years at least; it will be no surprise if we are still arguing about it in a decade’s time. At its most basic, Brexit means leaving the European Union. But the real debate is going to be about how the United Kingdom does that and what its relationship with the EU will be afterwards.

May has, understandably, kept her options open. Her government doesn’t yet know for sure what it actually needs from the exit talks. When David Davis, the Secretary of State for Exiting the European Union, spoke to the first meeting of May’s cabinet he emphasised two points. First, that Brexit had to be coordinated alongside the negotiation of trade deals with other countries. Secondly, that he’d like Secretaries of State to write to him setting out what their departments both wanted and feared from Brexit. It is worth noting, though, that many other countries will want to know what arrangement the UK has with the EU before deciding on what kind of trade deal to agree.

One clue as to what May is thinking is that she consistently talks about placing ‘controls’ on free movement, rather than ending it. Some have taken this as a sign that she is interested in a European Economic Area deal where free movement is accepted for work. The word on Whitehall is that one of the models Davis’s team is looking at is one in which the UK stays in the single market but with some more controls on freedom of movement. Intriguingly, one of those who worked with David Cameron on the renegotiation suggests that such a deal might be acceptable to the rest of the EU, but only if accompanied by a significant increase in the UK contribution to the Brussels budget.

What is certain is that Brexit negotiation will take place with hardline Tory Euro-sceptics watching anxiously from the sidelines. Some are convinced that victory will be snatched from them by fair means or foul. Last week, at a breakfast meeting between these MPs and two of Davis’s ministers — the former Welsh Secretary David Jones and Lord Bridges, who worked for both John Major and David Cameron — several MPs argued that the UK should get out of the EU as quickly as possible and then negotiate a new trade deal from outside the bloc. I’m told that this view did not find favour with the ministers.

It would not be prudent. But there is a danger that the UK might end up with a Norway-style deal with the rest of the EU, whereby we would have to obey all the rules of the single market despite having no say in making them. This would be a poor form of Brexit.

One leading Vote Leave figure is insistent that ‘Brexit doesn’t mean Brexit if we’re still subject to all single market rules, if we don’t control who comes here, and if we still pay into the EU budget.’

Essentially, any Brexit deal will face three tests: is UK law supreme over EU law; can the UK make its own trade deals; and is there parliamentary control over immigration policy? Ultimately, this democratic control is essential if public consent for relatively high levels of immigration is to be maintained.

An EEA-style deal would fall foul of this standard. The problem is that it might not be possible to negotiate the terms of a UK-EU free trade agreement within the two years allotted by Article 50. Even if the UK can persuade the EU to negotiate a trade deal during the talks — which would require overcoming institutional resistance from the Commission — the time frame could still present a problem.

The question then becomes: what should the UK try to do? Some argue that we should prepare ourselves for hard Brexit — to trade with the EU under World Trade Organisation rules. This would undoubtedly cause serious disruption to the economy.

Pragmatically, one could argue that the UK should move to EEA membership while the terms of this free trade agreement are hammered out. But the problem with this approach is that once the UK is in the EEA, the EU has no incentive to crack on with negotiating a deal, and our leverage would be limited. One possible remedy for this would be to use the EEA, but only for a specific and clearly defined period.

By the end of this process, the UK must have control on law, trade and immigration. Although the referendum was won by a relatively narrow margin, the issues of sovereignty and immigration were key to Leave’s victory. A final deal that did not properly address such priorities would fuel cynicism about politics.

The initial signs from the Brexit talks are mildly encouraging. May’s first European tour went better than expected. As one of her allies in cabinet observes, the fact that she is a new prime minister is helping her; she does not face resentment from other leaders over the fact that the UK decided to have a referendum in the first place.

The current security situation in mainland Europe has also focused minds on the need for continuing co-operation between the UK and other EU countries post–Brexit. When intelligence-sharing and counter–terrorism measures are being discussed, the debate moves far beyond the idea of ‘punishing’ the UK for leaving.

May’s only other commitment on Brexit is to make a success of it. To achieve this, she will have to show voters that leaving the EU doesn’t mean simply accepting all the rules of the single market while having no say in making them.