If Brexit were to be cancelled, at some point the EU Withdrawal Act (2018) would need to be repealed.
Would such a repeal be a precondition of any notification to revoke the UK's Article 50 notice? Or can such a repeal take place afterwards?
It's a good question, but I'm not sure there is a definitive answer to it. One press article says that at least May's government thinks it can legally revoke article 50 without prior parliamentary approval. On the other hand, the (successful) legal challenge against the government invoking article 50 without parliamentary approval argues against this (and is in fact a point remaked by ECJ's advocate general).
First, the government's position:
Sky News understands from senior government sources that - in pure legal terms - no legislation needs to be passed in order for any hypothetical revocation [of Article 50] to take place.
The government is understood to have received legal advice to that effect, with a ministerial source saying that legislation "might be needed politically, but not legally".
The source stressed that revoking Article 50 was not government policy, but it means a sitting government has the executive power to withdraw the notice at any point up to 29 March.
Or up to any mutually agreed extension date with EU, given recent developments, if the above reasoning is correct.
The government would not be legally obliged to pass an act of parliament in order to do this.
This had already been noted in the government's legal argument to appeal the Supreme Court decision to deny an appeal of the Wightman case's referral to the ECJ.
Government lawyers said: "For the issue of revocability to become live, parliament must first have directed the government, against the government's settled policy and against the popular answer provided by the referendum, unilaterally to revoke the notice."
It did not in that legal notice point to the requirement for an act of parliament.
Many in Westminster have presumed that because the Article 50 court case on triggering the EU exit process mandated an act of parliament, that one would be also required to withdraw it.
The BBC has a more detailed discussion on the matter. Apparently it's the Royal Prerogative that would allow May to do so, but this has already failed the test in court in the case of invoking article 50! So, in the opinion of ECJ's advocate general, a parliamentary decision in the UK is needed to revoke article 50 as well, with the caveat that the ECJ doesn't really gets to decide that:
Who decides? Theresa May or Parliament?
On this, the ECJ did not give a definitive answer. The court ruled that: "Revocation must be decided following a democratic process in accordance with national constitutional requirements."
The UK government can use the power known as the Royal Prerogative, which allows it to do certain things including deploying armed forces, granting honours and altering international treaties without consulting Parliament.
So it is possible in theory, but unlikely, that Mrs May would be able to revoke Article 50 without giving MPs the chance to vote on it.
She has no plans to do so though, saying: "I do not believe that we should be revoking Article 50."
There are also limits to the power of the Royal Prerogative, and those limits have been tested during the course of the Brexit process.
Their use to activate Article 50 was challenged by Gina Miller at the beginning of 2017.
The Supreme Court ruled in her case that the government could not trigger the EU exit process without bringing it before Parliament.
Because an act of Parliament had been required to trigger Article 50, the ECJ advocate general said: "It is logical, in my view, that the revocation of that notification also requires parliamentary approval."
This does not mean it is a completely settled matter though.
As independent research group The UK in a Changing Europe points out: "Neither the advocate general nor the ECJ has the power to rule on the UK's constitutional arrangements."
Personally, I'm inclined to think the the UK's High Court would follow its own precedent, which stated among the principles that:
The Court noted that “the powerful constitutional principle that the Crown has no power to alter the law of the land by use of its prerogative powers is the product of an especially strong constitutional tradition in the United Kingdom…” (para.86).
... unless that power is vested in the Government by law specifically for some purpose. It looks like the Withdrawal act doesn't do that for outright revocation. I'll also note that the Withdrawal act itself does use the word "revoke" many times (i.e. grants that power to the government), but with regard to subordinate legislation. Had it allowed the government to revoke the whole act, I'm sure it would have been a point noted by some legal analysis.