Elections for the European Parliament are taking place across the UK this Thursday, nearly two months after the country was supposed to leave the European Union.

How should Brits cast their surprise ballot?

Usually turnout is very low, so the first thing is to vote and by doing so to show that Europe matters. For, in effect, this is a continuation of the referendum. The second thing is to remember that this is a much more proportional system than Westminster, so you don’t need to vote tactically. Better to vote strategically.

The polling points to a disintegration of British politics, with both the main parties haemorrhaging their support. Pro-Europeans, the so-called remainers, blame the sharp populist rhetoric and dubious funding of the Brexiteers. In fact, the remain side has been unable to get its act together and is on course to lose again. Why this is so is by the far the most important issue of the day.

If you are for Brexit there are two options. You can vote for the Brexit Party and help Nigel Farage build it in preparation for the next general election. He intends to model it on the Five Star Movement in Italy, with its networked membership, internet voting and de-facto centralised power that gives its leader almost unbridled freedom of action while appearing modern and democratic. Its politics, however, will be that of Italy's far-right Lega party, thus fusing the poisonous mix of the country's coalition government into a single force.

The Brexit Party wants a ‘No Deal’ exit from the EU. Farage says that when this happens “the EU will come running” to secure British trade. If you believe this, he is your man and you should vote for his candidates. So far he has achieved the almost impossible: the Brexit Party is polling at over 30%, well ahead of everyone else.

The leavers’ alternative is to vote for the Conservative Party and support the prime minister’s deal, which keeps the UK in the EU’s regulated space for trade. It isn’t a “real” or “clean” Brexit (but then there cannot be any such thing as I’ve shown). But it is a Brexit. The substantive problem with it is that the UK becomes a ‘rule-taker’ – so what is the point? The prime minister’s staggering incapacity to communicate her answer to this question has made her proposal uniquely unpopular. In this sense it brings the country together. Should it pass in the House of Commons next month, as May hopes, when she puts it forward for a fourth time, a general political implosion is likely to intensify. However, by all means, vote Tory if you disagree. In what is a devastating rebuke to the country’s historic ruling party, it seems only between 10 to 20% will do so.

What if you want to vote to remain in the EU?

In Scotland and Wales the answer is clear. In Scotland, which has six MEPs, you can either help elect a third SNP MEP, or a first Green. In Wales, with four seats, Plaid Cymru and its new leader Adam Price look like the best option.

In England, the country responsible for Brexit, it is chaos. There is a choice of three small unequivocal remain parties competing against each other while some of Labour’s candidates, for example Eloise Todd and Laura Parker, are the most outstanding advocates for staying in the EU.

Of the three remain parties the newest is Change UK. In terms of freshness, it is the remain equivalent of Farage’s Brexit Party. Its leaders too have achieved the astonishing – by doing as badly as he is doing well.

A Best4Britain interactive webpage that projects outcomes in terms of electing a candidate shows that if you want to join forces with other remainers to prevent a Brexit Party sweep you should not vote for ChangeUK. But if you just want your vote to be counted, by all means go ahead.

Their fate is far from irrelevant. Change UK shares the same problem as the remain movement – it is not serious about change.

Nor as yet are the Liberal Democrats, who the polls say are the most popular of the three. They used to be the party with the surest grasp of the need for democratic reform but have abandoned this distinction under their current leader, Vince Cable. However, they retain an experienced ground operation and a familiarity that makes them seem credible.

In effect they have become the party of a return to the status quo – of life before Brexit. They are in danger of becoming the true Conservative party and will do relatively well. If you too just want Brexit to go away, if you yearn for a return to 2014, then they are your party.

Third, although they should be the first of the three remain parties, are the Greens. Their historically far-sighted response to climate and environmental breakdown means they have a credible pro-European case on that front.

Importantly, how well each of these parties does in this election will help shape the future of the UK’s pro-EU movement. If the Lib Dems soar and Greens end up as also-rans, then the remain movement will find itself tethered to a deeply unpopular status-quo, just as it sinks, and a party with an undeniable record of misleading voters.

If the Greens are the surprise success story of this election, then they will boost the argument that participating in and changing the EU is about building a novel, democratic future. To vote Green is to give a platform to those who will argue to “remain and revolt” as Scottish Green lead candidate Maggie Chapman has put it. A call that taps into the democratic energy of Brexit, steering it towards real change.

If, like me, you wish to sack the establishment and remain in the EU, then the Greens are your shout.

So too are some individual Labour candidates. But the party itself seeks to appeal to both Leave and Remain voters – which can be an honourable and essential ambition – by playing down the importance of Brexit. Its leader regards Brexit as much less important than getting a Labour government. What he doesn’t see is that only by opposing Brexit and retaining working class support is there any hope of achieving a majority in the House of Commons.

The obvious way of achieving this is to support voters who want to “Take back control” – the slogan of Brexit – by proposing deep and lasting democratic reform of Westminster, the economy and local government – while showing that Brexit will not achieve this.

Unfortunately, Jon Trickett, the most politically experienced member of Labour’s Shadow Cabinet, who is in charge of democratic reform, while genuinely anti-elitist, supports leaving the EU and opposes another referendum. In effect Labour’s reforming spirit has been depoliticised – to the frustration of many Corbynites, such as Paul Mason.

The strongest Labour message is that they are the only party to beat Farage. They have gone negative not positive. Instead, they should be beating him on his own chosen ground where his argument is most compelling – his call for a “democratic revolution” .

If you are a remainer and feel that the lesson of the 2016 referendum is to vote with your heart then that is what you should do on Thursday.

At the same time remainers should be thinking now about the lessons to draw from the shambles of their ‘opposition’ to Brexit. For there is a reasonable chance that there will be a general election soon.

It seems certain that Theresa May will resign and the Tories will elect a new leader before the summer. It is likely this will be a male Brexiteer who will then confront a parliament where, just like May, he does not command a majority. If he is brave he will call an election. If he is wise he may attempt to shape his own version of Brexit, but the likelihood is it will be voted down and he will have an election forced on him.

If so, how can the millions of remainers avoid a repetition of this week’s scenario?

Not by waiting. We have to start by facing up to the fact that the remain parties are incapable of coming to an agreement from above, whether or not this includes the Labour Party, as hopefully it will. Therefore a public process, such as running primaries, should settle matters from below. This is the only alternative to ensure that there is only one wholehearted remain candidate in any constituency. That is particularly important, as UK general elections – unlike this week’s Euro elections – are fought on the archaic, winner-takes-all, imperial system.

The differences between the various motives for remain are considerable. They can’t be resolved by administrative means. So let remain supporters hear and express the arguments for themselves and choose who they want to represent them in each constituency.

So my message to my fellow remain supporters is: vote with your heart but for goodness sake start to use your heads.