Timeline outlining all the updates as they unfolded on the Brexit process, and the likelihood of it actually happening
Update as of 28 November 2018:
Even if the UK public and/or Parliament expressed a strong view that the original decision to leave the EU was a mistake, the process of withdrawal as a matter of EU law has begun and is probably irreversible in terms of practical politics, whether or not it is irreversible as a matter of strict EU law (which is a debatable point).
Even if all Member States, including the UK, concluded that Brexit had been a mistake and should be reversed, it is extremely unlikely that the 27 other Member States would agree to a simple cancellation of the decision to leave and allow the UK to remain a Member on its existing, highly preferential, terms; it would be likely that re-entry would be permitted only on substantially changed terms (including, in particular, abolition or diminution of the UK’s special rebate on contributions) and it is likely that it would be politically impossible for the Government to agree to those terms.
So, although nothing is impossible, should circumstances change and the political will be found in all 28 Member States for simple cancellation of Brexit; the political context at present makes it appear that there is no likely scenario in practice other than the UK leaving the EU.
The Court of Justice of the European Union has now been asked to rule whether the UK could unilaterally withdraw its Article 50 notice to leave the EU; if the Court decides that this is a possibility, it would be theoretically possible for the UK to insist on remaining in the EU on its present terms. Whether that is a practical possibility is again a matter of politics not law.