The Article 127 in question is not a provision in the EU treaties. The provision is from the agreement for the European Economic Area (EEA). The EEA is a combination of the EU member states, as separate signatories, and three of the four members of the European Free Trade Area (EFTA). In essence, membership of the EEA means membership of the single market.

Article 127 is a straightforward, rather bland exit provision:

Each Contracting Party may withdraw from this Agreement provided it gives at least twelve months’ notice in writing to the other Contracting Parties. Immediately after the notification of the intended withdrawal, the other Contracting Parties shall convene a diplomatic conference in order to envisage the necessary modifications to bring to the Agreement.

The significance of this is in its possible implication: leaving the EEA is a separate and distinct act from leaving the EU. And if this is the case, then the UK leaving the EU does not necessarily mean leaving the single market in tandem. It should be recalled that the referendum question posed on 23 June 2016 was about the UK’s membership of the EU, not the EEA. A contention can therefore be made that the “leave” result of the referendum offers no political mandate for leaving the EEA. Brexit can still mean Brexit but it might not mean the UK turning away from the single market.

Furthermore, if the UK can remain within the EEA whilst leaving the EU then the Conservative government can achieve both its 2015 general election manifesto commitments of respecting the referendum result and “safeguarding” the UK’s position in the single market.

There would also be further scope for the House of Lords (and possibly the Commons as well) to block or delay any Brexit legislation which did not keep the UK within the EEA. The constitutional convention that parliament will not hinder any legislation which has a mandate — either from a general election or a referendum — would not apply to the UK ceasing to be a member of the EEA.

[...] Any legal case based on Article 127 is therefore still at a rudimentary stage. There is no challenge as yet to the government and there is no claim for the government to answer, less still any developed and formal legal argument. In contrast to the advanced Article 50 litigation, which in a few weeks will arrive before the Supreme Court, the Article 127 argument is nowhere near being litigated. [...]

If the government decides not to make a separate Article 127 notification, and says simply that it is implicit in giving a notification under Article 50, it is then tough to see how any UK court could gainsay this view (unless parliament by then has provided otherwise), and it is also difficult how this could get before the EFTA court which rules on disputes about the EEA agreement.

Article 127 also faces a problem by reason of the provision just before it in the EEA agreement. Article 126 provides that the EEA comprises the EU members (which the UK will presumably not be after Brexit) and three specific EFTA members (Norway, Iceland and Liechtenstein). Once the UK leaves the EU, it also departs from those listed in Article 126: the question is then whether it thereby departs from the EEA agreement as a whole, even though it is a separate signatory. And although Article 126 does not expressly say that it a closed list of EEA members, it does have the appearance of an exhaustive provision. [...]

There are, however, two ways Article 127 could perhaps make a substantial difference — but as a shield rather than a sword. One is if the UK government wanted the basis for legal (or legalistic) cover for remaining in the single market whilst leaving the EU. The problems posed by Article 126 could be fudged in this scenario.

The other is if parliament wanted constitutional cover for slowing down any Brexit legislation which did not keep the UK in the single market, arguably because there is no mandate for leaving. A parliamentary vote on UK remaining in the EEA may have a different result to one on the Article 50 notification. Parliament could even expressly legislate that the Article 127 notification cannot be given. This would then create a delicious international law problem of whether giving an Article 50 notification to leave the EU implicitly also means giving Article 127 notification to leave the EEA. This would presumably would have to be determined by the EFTA court. [...]