Editor's Note: (Beth Oppenheim is a researcher at the Centre for European Reform in London. Follow her on Twitter @Beth_Oppenheim. The opinions expressed in this commentary are those of the author.)
(CNN) The UK's 2016 Brexit referendum was meant to put the vexed question of Britain's relationship with Europe to bed forever -- it didn't.
The debate about the UK's relationship with the EU has continued to rage since Britons voted 52% to 48% to leave the bloc.
Fears of a damaging, haphazard Brexit are growing with every day that passes without a withdrawal agreement.
Hopes of a Brexit breakthrough at this week's European leaders' summit have been dashed. So "Remainers" -- as pro-EU supporters are known -- are now throwing their weight behind a growing campaign for a rerun -- the People's Vote.
They're hoping to draw tens of thousands from around the country to another march through London on October 20 to press their case.
But the chances of a new EU referendum are slim: there are substantial political and practical obstacles, and time is running out.
The arguments for and against are finely balanced.
People's Vote supporters contend that voters should get a say on the final Brexit deal, especially as it is likely to be different to what was promised two years ago.
The 2016 referendum campaign atmosphere was febrile and dishonest -- some even suspect foreign interference. Furthermore, as the negotiations to leave have worn on, the difficult trade-offs involved with leaving the EU have become much clearer to Britons. There is a growing demand for a new referendum from politicians across the political spectrum, including from the governing Conservatives.
Former Prime Minister Tony Blair and former Deputy Prime Ministers Nick Clegg and Michael Heseltine made an intervention this week in the German newspaper Die Welt, calling for a referendum. One millionaire owner of a well-known plumbing company has put up bright yellow billboards around London exclaiming: "Bollocks to Brexit -- it's not a done deal". Bookmakers have the odds of another referendum at 2/1.
However, Prime Minister Theresa May -- who campaigned to stay in the EU -- has said a further referendum would be a betrayal of British democracy. Both Mrs May and the opposition Labour Party leader Jeremy Corbyn say the original result should be respected and fear punishment at the ballot box by Leave voters if they don't.
The 2016 plebiscite attracted many who felt forgotten by the political establishment.
EU membership is an incredibly complex and emotive question. This toxic combination made the referendum vulnerable to oversimplification and populist rhetoric. Such a weighty issue should never have been put to a simple in-out vote in the first place -- so repeating the exercise would make no sense. And ultimately, there's no guarantee that a new referendum would produce a different result
In practical terms, the time needed to hold a new referendum has all but run out. Staging a new vote would take a minimum of 22 weeks including legislation and campaigning. But fierce debate about the wording of the question and other details suggests it would take longer.
It is not clear whether the choice would be between versions of Brexit or whether the ballot paper would include an option to stay in the EU. Some have suggested a three-option vote, while others have considered a two-stage referendum. At the very least, the government would need to have a prospective Brexit deal for people to vote on -- and that might not be clear until the end of the year. That means it would impossible to stage a referendum before the UK is scheduled to leave the EU on March 29, 2019.
The UK could seek an extension to the two-year legal process for leaving the EU, but that would require the unanimous agreement of the other 27 EU member-states.
A short extension of a few weeks would be manageable, but consensus on anything longer would be much more difficult as it would disrupt the European Parliament elections at the end of May 2019.
The European Parliament has already agreed to re-allocate the UK's seats to other countries, including France, which has proved tough in the Brexit negotiations.
The prime ministers of Malta and the Czech Republic have voiced their support for a new EU referendum, but other EU leaders have said they respect the original result even though they are unhappy about it.
The EU is already struggling to respond to the rising tides of Euroskepticism on the continent -- a second lost referendum could help the populists. There is also little sign that EU officials are preparing for a possible re-run vote.
Even if the practical obstacles for a new referendum could be overcome, there is no political will to do so. May has repeatedly ruled one out. There is support for one in the Labour Party, but it would far prefer an election.
A perfect Brexit storm could create the right conditions - if the prime minister failed to agree an exit deal with the EU, or if her deal was rejected by parliament, it might become an attractive option to hand the issue back to the electorate to decide. But the last time Theresa May changed her mind about holding a vote in 2017 she lost her party a parliamentary majority -- she may not be so keen to do it again.