Whatever Theresa May or David Davis might say (as he did this week), the UK is not going to be completely out of the EU with a negotiated agreement by 29th March 2019. Any agreement will require longer than the 18 months until March 2019 to be put into practice, let alone negotiated. The only way the UK can be out of the EU by March 2019 is if it crashes out with No Deal (more on that here).

But what are the options to stagger the UK’s exit or to buy more time for negotiations? Here I propose four terms to describe what could happen.

Article 50 Extension Period
Is the UK legally still in the EU? Yes
Does the UK still have MEPs, a Commissioner? Yes
How long would it last? The extension would be time limited (one presumes a couple of years), but could then be extended again by the same procedure
Can this be combined with other options? Yes, with a Transition Period and/or with an Implementation Period
How would it work? The two year Article 50 negotiation period can be extended with the unanimous agreement of the rest of the Member States of the European Union, at the request of the exiting state. Were this to happen it would cause the minimum of legal and political disruption – nothing would formally change in the UK-EU relationship. It would provide short term stability and reassurance to business. Were the UK to somehow decide to stay in the EU after all, this option means that is as simple as can be. CEPS has more detail on this in a paper here.
What are the downsides? The rest of the EU is keen to have the UK out now, and this would just prolong the eventual decision. The UK would also keep a Commissioner and MEPs, which could be strange at a 2019 European Parliament election. UK would also participate in the next Financial Perspectives – possible budget headache. Eurosceptic MPs would freak out at the whole idea.

Prolongation Period
Is the UK legally still in the EU? No
Does the UK still have MEPs, a Commissioner? No
How long would it last? The extension would be time limited (again one presumes a couple of years), but a procedure would need to be devised as to how to lengthen it (would need a majority of Member States somehow to prolong further)
Can this be combined with other options? Yes, with a Transition Period and/or with an Implementation Period
How would it work? This is similar to the Article 50 Extension Period, in that it leaves the UK’s relationship with the EU unchanged in terms of everday procedures. The UK would remain a full member of the Single Market and the Customs Union, but would do this as a non-EU Member, and would have no representation in the EU institutions. It would continue to contribute into and finance projects from the EU budget as now.
What are the downsides? Even a deal where so little changed with Single Market and Customs Union membership would take some negotiating. Calculating how the UK would contribute to the EU budget as a non-EU Member State would be a headache. And a system to prolong the prolongation period (if necessary) would need to be agreed. It would be harder to agree to this than to an Article 50 Extension Period. That the UK would be formally outside the EU might reassure Brexiteers a little, but they would still scream “Brexit in name only!”
[Update 26.10.17, 1500] Seeing what Barnier adviser Stefaan De Rynck has said today, it strikes me that what he calls “Transition Period” is actually what I here call Prolongation Period.

Transition Period
Is the UK legally still in the EU? No
Does the UK still have MEPs, a Commissioner? No
How long would it last? The transition would have to be time limited (again one presumes a couple of years), but a procedure would need to be devised as to how to lengthen it (would need a majority of Member States somehow to prolong further)
Can this be combined with other options? Yes, with any of the other options
How would it work? Here the UK would be more out of the EU than in the Prolongation Period scenario. Some things would change – perhaps that the UK would already cease to participate in some EU programmes, or parts of the EU budget. Exactly how different to the status quo this would be would depend on the negotiations during the Article 50 period. It is unlikely the UK would be outside the Single Market and the Customs Union though.
What are the downsides? The EU worries about the disruption this option would cause – everyone would have to adjust to the start of the transition period, and then adjust again at the end of this period. Trying to negotiate this would be highly complicated, not least as it would have to be done before the UK’s final and permanent trading status with the EU were known. British Eurosceptics might be reassured that this would look a bit more like a Brexit they have been convincing themselves they want to see.

Implementation Period
(note: when Theresa May talks about an Implementation Period I am unsure if she means this, or what she means!)
Is the UK legally still in the EU? No
Does the UK still have MEPs, a Commissioner? No
How long would it last? Phased, on a case by case basis, or sector by sector. It would be known what the destination for the UK would be (to be outside the Customs Union for example), but actual Customs Controls would start a number of years later. A procedure would be required to resolve disputes in the case the UK did not stick to its commitments.
Can this be combined with other options? Yes, and it must be. A deal on the UK’s permanent relationship with the EU is next to impossible to agree by March 2019.
How would it work? The final deal with the EU would have been struck, but not all of it would come into force immediately, as things like Customs Controls, or new food sanitation standards, will need time to actually practically be done by the UK. Each of these aspects would have its own implementation timetable.
[Update 26.10.17, 1100] Fabian Zuleeg talks of 5 years for this
What are the downsides? This only comes right at the very end – it is the only one of the four options here that takes place after the UK’s final relationship with the EU has been hammered out. Brexiteers could live with it, but it is inadequate on its own.

[UPDATE 26.10.17, 1730]
Pete North has another take on the terminology to use:

From now on I am avoiding the word "transition" and sticking to "interim" then implementation. Politics/media have rendered the word useless

— Pete North (@PeteNorth303) October 26, 2017