Theresa May, the UK prime minister, has said that there will be no new Brexit referendum “in any circumstances”. This came in response to former education secretary Justine Greening’s claim that a fresh plebiscite is needed to end the parliamentary “deadlock” over what sort of Brexit deal the government should be pursuing.

Calls for a referendum to approve or reject the government’s Brexit deal have typically been voiced by those – like Greening – who are sympathetic to the UK’s continuing membership of the European Union. The People’s Vote campaign for just such a referendum is backed by the pro-EU group Open Britain. Unsurprisingly, such demands are vulnerable to the accusation by Leavers that they are an attempt to undo the result of the 2016 referendum.

Nonetheless, Brexit supporters are expressing their increasing discontent with the government’s proposals on the UK’s future relationship with the EU. Some may therefore now join Remainers in viewing a new referendum as the only way to avoid the prime minister’s vision of Brexit.

The impediments to another referendum are, however, evident.

Leaving aside all other practical considerations, a central difficulty would be in specifying the referendum question. The decision back in 2015 to change the referendum question from one that would elicit a “Yes/No” answer to a “Leave/Remain” response was not uncontroversial. But at least voters were presented with a binary choice between the status quo of remaining in the EU or change in the form of Brexit. The problem now is that Remainers and Leavers have radically different views of what the status quo option should be.

For Remainers, it’s self-evident that the status quo is continuing EU membership. In their view, voters should be asked whether they want to accept the deal negotiated by the government or to reject it in favour of remaining in the EU. But for Leavers, this ignores the new status quo created by the 2016 referendum – namely that the UK has decided to quit the EU. For them, the options on the ballot paper could be between leaving with “no deal” or accepting the Brexit deal agreed with the EU.

A referendum could depart from the binary selection model and give voters a three-way choice. So voters would have to select between remaining in the EU, leaving the EU with no deal or accepting the government’s agreement with the EU. The obvious risk is that no single option commands more than 50% of the popular vote. Imagine a scenario in which the electorate voted in the same way as in 2016 – 48% backing EU membership – but the Leave vote splits in half with 26% supporting the negotiated withdrawal agreement and 26% wanting a no-deal Brexit. There would still be a majority vote to leave the EU but the option of remaining in the EU would have significantly more votes than either of the leave options. This would only intensify the political deadlock, not resolve it.

It’s also just not obvious that there is any time for a new referendum. The 2016 referendum was held almost exactly 13 months on from the introduction of the European Union Referendum Bill into the House of Commons. We are now just eight months away from the UK’s departure from the EU. The bill itself took nearly seven months to become law. Legislation would have to be rushed through parliament to make a second vote possible.

The Electoral Commission’s best practice for the conduct of referendums also stipulates that referendum legislation should be clear at least six months before it is required to be implemented or complied with by campaigners. This is not six months before the referendum is held but rather six months before campaigning gets underway. The Electoral Commission recommends a ten week referendum period during which campaigning and campaign funding is regulated. With the Electoral Commission finding that the Vote Leave campaign broke campaign finance rules during the 2016 referendum, there is a clear risk that a rushed referendum campaign could give rise to more accusations of wrongdoing.

There is also a wider question of whether another referendum is simply contrary to the UK’s constitutional tradition in which parliament is sovereign, not the people. The difficulty here, however, is that the UK’s constitutional process evolved under EU membership with the European Union Act 2011, binding governments to hold referendums to endorse or reject the outcomes of certain treaty negotiations at EU level. The 2011 act is repealed under the European Union (Withdrawal) Act 2018 and the referendum requirements under the 2011 act were never triggered when it was operational. Nonetheless, a referendum on a withdrawal treaty which sets out the framework for the UK’s future relationship with the EU is not inconsistent with the constitutional reforms of the 2011 act.

The UK now finds itself stuck between a model of parliamentary democracy that – thanks to the Fixed-term Parliaments Act 2011 – keeps this government in power but potentially unable to command majority support in the House of Commons for its Brexit plan, and the option of a referendum that is unlikely to resolve the political deadlock. If the UK is to avoid becoming ungovernable, something is going to have to give.

This article was originally published on The Conversation. 

Kenneth Armstrong is Professor of European Law and Director of the Centre for European Legal Studies at the University of Cambridge.