We are where we are because of a referendum. The result of which seemed likely to mean there would be no more European elections in the UK. Instead, it has produced a highly charged contest, featuring two completely new political parties formed for the purpose of contesting it. With this in mind, how do we make sense of a strained and turbulent UK political system?

The exercise in direct democracy that took place on 23 June 2016 has triggered a prolonged period of political ferment that our predominantly representative democratic system has struggled to contain. Referendums have taken place before in the UK – there have been 13 on major issues since 1973. But the 2016 public vote on EU membership was different. It’s not so much because it produced a result to which the government of the day (with some licensed dissenters) along with majorities in both Houses of Parliament, were opposed. Governments have lost referendums before, including over devolution in 1979 and 2004. The real complicating factor was that the referendum result required positive action, which would fall to these largely Remain-inclined institutions in Whitehall and Westminster. The position was made more difficult by the fact that it was never clear, precisely, what Leave meant on the ballot paper.

In fact, the government was under no legal obligation to do anything at all. Despite this, a powerful prevailing wisdom, since the vote up to the present, has created a transcendent political imperative to deliver. Even those most opposed to the idea of leaving the EU tend not to reject the referendum result, but instead propose a “People’s Vote” with Remain as an option. They implicitly accept that the referendum has a special force, overriding that of the organs of representative democracy. The argument about whether or not it is appropriate to hold a further vote is in effect a proxy for disagreement about EU membership itself. Even though, in theory, Article 50 could be revoked by government or parliament, this course of action remains off limits for most in the Remain camp. These aspects of the Brexit episode, and the way in which they pertain to the relationship between direct and representative democracy, are manifesting themselves in the European parliamentary election campaign.

This is most obviously demonstrated in the policies on the central issue of Brexit taken by the various parties. Their stances are not in every case as easy to discern as might be imagined, but there is sufficient information in the public domain to make the following assessments.

What might be termed the pro-Brexit parties differ in their precise prescriptions. The Brexit Party, which looks set to win the most votes and seats, will not be publishing a full manifesto in advance of the European election. But its central position appears to be that the UK should leave the EU without any deal, or with what its leader, Nigel Farage, has described as “a WTO deal”. There seems to be some allowance for a deal, alongside the WTO terms policy (pledge 3), as Brexit Party MEPs are allowed to take part in negotiations with the EU (pledge 1). They also pledge to prevent a cross-party deal between Theresa May and Jeremy Corbyn (pledge 2: now a dead issue, it seems); and refuse the 39 billion euro exit fee (pledge 4).

For its part, UKIP, now seemingly supplanted by the Brexit Party as the main radical Eurosceptic party, supports immediate unilateral exit from the EU. The UK, under this plan, would then give the EU a choice between trade without any tariffs, or trade under WTO rules.

Already there seems to be a difference, at least of emphasis, between the two parties most firmly associated with Brexit. With a different line again, the Conservative Party, or at least its current leader, is committed to securing the support from the parliament for its present exit deal. The DUP and UUP both support Brexit, but not the Northern Ireland backstop. One lesson to draw is that Brexit can appear in different forms, whereas referendums normally present binaries. So if one or both of the choices contains diverse possibilities, a referendum might not help resolve a difficulty – and could make it worse.

Labour seeks to pitch itself both to Leave and Remain supporters. Its policy at the European election, at least according to the leader, is to seek a different deal to that secured by Theresa May, including presence in a customs union, and adherence to much of the single market. The party holds that if it cannot achieve this outcome or a General Election, then a further referendum is the fall-back option. This complex formulation seems so far not to be securing much support from the electorate. Appealing to both sides may have been reasonably successful in the 2017 election, but it seems to have lost its effectiveness as an electoral tactic. Picking sides is important and has to be done convincingly and credibly. Otherwise, as with the Conservative Party, it seems unlikely to succeed. Such is the divisive impact of the 2016 referendum, which has become only more intense over time.

Change UK’s manifesto is called "Charter for Remain". However, rather than simply reversing the decision to leave, it favours holding a People’s Vote on any exit deal, campaigning for Remain. Any Change UK candidates elected as MEPs would seek to block in the European Parliament's approval of a deal on which the UK had not held a referendum. The Green Party supports a further referendum, in which it too would campaign for Remain as do the LibDems, Plaid Cymru, the SNP  and, in Northern Ireland, the Alliance Party.

Nearly all pro-Remain parties then, express this position through support for a further referendum. Sinn Fein is slightly different, advocating an arrangement for the whole of Ireland - the North and the Republic, to remain in the EU. The only party that seems to be supportive of a straightforward revocation of Article 50 is the Northern Irish SDLP.

Accepting the idea that a referendum has a special legitimacy remains pervasive. Yet it seems that more than six million people who signed the petition earlier this year calling for the cancelling of Article 50, do not agree. This petition is the largest of its type in history. The second most popular ever was in favour of another referendum, with around 4 million signatures. The idea of a further popular vote is represented by a multiplicity of parties - yet voters looking for a party that wants to stop Article 50 without a referendum, will only find one on the ballot paper if they are in Northern Ireland.

The incorporation of direct democracy into the UK constitution has, so far, largely denied an outlet for this view, despite manifest mass support. The 2016 referendum was a vehicle for one previously marginalised preference. It is now having the perverse subsequent effect of excluding a another outlook.

Dr Andrew Blick is  Director of the Centre for British Politics and Government and a Senior Lecturer at King's College London, He is the author of Stretching the Constitution: the Brexit shock in historic perspective (Hart/Bloomsbury, Oxford, 2019).