Under Theresa May's ill-fated Withdrawal Agreement Bill (WAB), MPs would have been given the chance to vote on whether to hold a second referendum. Although that Bill has now been put on ice, at least one of the hopefuls in the Tory leadership contest - Sam Gyimah - has come out in support of a referendum, and the Labour leadership is under increasing pressure to make a similar commitment following its poor performance in the European elections.
As the debate surrounding Brexit continues, we consider the impact if a second referendum was back on the table and what it would mean for businesses.
What needs to happen for there to be a second referendum?
Should the WAB have been introduced into Parliament, and passed in a form which included the vote on a second referendum, the government would have been required to make provision for that vote to be held. If MPs voted for a second referendum, further legislation would then have been needed to put in place the detailed rules for how that referendum was to be carried out.
In the absence of the WAB, MPs could decide to vote on holding a second referendum anyway - through Labour using one of its opposition days to schedule a debate, for example. Alternatively, the new Conservative PM, or in the event of a snap election a possible Labour PM, could make a referendum government policy.
If there is a second referendum, what will the public vote on?
This is currently unclear. Theresa May stated it would be a vote to 'confirm' her deal - suggesting it would have been a choice between her Withdrawal Agreement and remaining in the EU. However, different MPs will have different views and the question to be put to the public will be the most important area for disagreement after whether or not there should be a referendum in the first place.
Is there enough time for a second referendum?
Change UK - the party formed by 11 former Conservative and Labour MPs - has claimed that there isn't enough time for a second referendum before the UK is due to leave the EU on 31 October.
According to the Constitution Unit at University College London, it takes a minimum of 22 weeks to organise a referendum. That timeline includes the time taken to pass the legislation necessary to hold the referendum, testing by the Electoral Commission of the question to be asked, and time for the regulated campaigning period currently required under existing legislation.
There is now less than 22 weeks until 31 October, in theory time has run out, although the EU may grant an extension to Article 50 to allow the referendum to take place. Alternatively, Parliament could seek to compress some of the stages outlined above, but that would be difficult given the controversial nature of a referendum (and particularly the question to be asked) and the result of a rushed referendum might have less credibility.
What would a second referendum mean for business?
Businesses - and business groups - have been extremely vocal in their frustration at the lack of resolution, and have called for stability to enable them to plan for the future. Arguably, a second referendum could prolong this uncertainty, and leading business figures have been split about whether it would be a good thing for the UK economy.
In April, the president of the CBI, John Allan, said that, while the CBI didn't have a position on a second referendum, his personal view was that the only way to get a resolution was to "go back to the people and have a second referendum to see whether people still feel the same way they did almost three years ago."
However, last year, chief executive officer of TheCityUK, Miles Celic, said: "Business likes certainty and I can't see how discussion of a second referendum helps create that certainty."
That said, in January this year, over 170 business leaders signed a letter in The Times backing a campaign for a second referendum on Brexit, saying it was the only way to prevent a "chaotic crash-out from the EU".
What is common though, is the demand for certainty. Following the failed cross-party talks earlier this month, business groups including the CBI and IoD have been unanimous in their views that the continuing uncertainty is bad for business.
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