If Britain leaves the European Union but retains its membership of the single market and the customs union, has it really left? Barry Gardiner doesn’t think so. Labour’s shadow trade secretary, writing for the Guardian, argues that to satisfy those who voted Leave, Britain must regain control of its own borders – forcing it out of the single market in order to lose free movement rights – and its own laws, forcing it out of both the customs union and single market to avoid regulatory harmonisation.

Jeremy Corbyn has argued that single market membership and EU membership are one and the same, as has Caroline Flint. They have kept the options open on the customs union. Are they right?

As I wrote yesterday, it’s hard to explain what drove Britain’s Brexit vote without conceding that objections to the rules of the single market played a significant role. Gardiner is undoubtedly right to say that two of the biggest drivers of the vote were control over borders and laws, both of which cannot be achieved while remaining within the single market. Neither can the third biggest driver, which was more money for public services in general and the NHS in particular – that £350m a week. Because if the United Kingdom retains its single market membership, it will continue to “send money to Brussels”.

There’s a “but” coming, though, and it’s a big one. The first problem is that while the majority of people who voted to leave did so for reasons that cannot be fulfilled if we remain in the single market, those votes weren’t enough to take Britain out of the European Union. Leave only triumphed because it also secured the votes of people who thought it would take the country out of the political project but would retain a Norway-style arrangement.

The second is that those three big mandates cannot be reconciled with each other. If the United Kingdom leaves the single market and the customs union, then the promise of more money for the NHS will be difficult, perhaps impossible, to deliver, at least not in the way that people envisaged. (When people said they wanted £350m extra in the NHS, they didn’t mean “in order to pay for drugs that are more expensive, to recoup the cost of our new regulatory regime and to plug the recruitment gap left by EU citizens with high-priced locums”. They meant that the NHS would do everything it does now and more, not run to stand still.)

The great success of Vote Leave was in presenting a whole menu of contradictory options as if they could be served on one dish. But you cannot have the Extra Hot and the Lemon & Herb on the same piece of chicken. You have to choose. The big failure of the political class has been not to advocate for one of those options over the other. (Theresa May has effectively been running on a ticket of “Extra Hot, Lemon & Herb, and the French will pay for it”.)

You cannot have a Brexit that unlocks trade deals with India and the rest of the BRICS (five major emerging national economies) and reduce the uncontrolled flow of people from elsewhere around the world to the UK. You can’t have a more generously-funded public realm and pursue a Brexit that makes everyone poorer. You have to choose.