Oh, well you may have a major problem there I'm sorry to say. The history of the withdrawal article (now Article 50) in the EU integration process goes back to 2004 with the failed Constitutional Treaty of OTL (and it seems from this TL too). In that treaty it was
Article I-60 which also had a two year negotiating period for withdrawal. Article I-60 then evolved into Article 50 of the Treaty of Lisbon almost unchanged.
Butterflies can definitely explain Article 50 being a three year procedure, but the problem there is that there seems to be very little to suggest that anyone
ever suggested a period other than 2 years.
I suspect a better option would be that rather than for the Article 50 procedure being now 3 years (it would likely remain at 2 years), that the new Burnham government made one it's first priorities an extension of the time to 3 years because:
(a) there was a change in government with a change in priorities concerning the negotiations and outcomes
(b) Burnham would want the best deal achievable for the UK and given that he wants more distance from the EU (and possibly unlike the current lot, might well recognize that the complexities of the process might require more time to negotiate) will want more time to negotiate it
Now unlike OTL, this Brexit is coming not towards the end of an EU budget cycle (2020) and before the next European Parliamentary elections (May 2019) but started at the beginning of one (the 2007-2013 budget cycle) and is set to come to an end (October 2009) after the next European Parliamentary elections (June 2009) anyway. This makes the exit a bit messier than in OTL but also means that Burnham could push for an extension anyway since an extension won't create the issue of the UK participating in the June 2009 European Parliamentary elections as an exiting member state (that issue would exist already) and can argue that more time would help to satisfactorily resolve all outstanding issues. So likely the remaining member states agree to a new apportionment for the European Parliament between 2007 and 2009 to take effect
after the UK exits and a delay to 2010 won't materially affect this - the 2009 elections happen as they should (but likely without the Lisbon treaty taking effect in time so it remains at 736 MEPs rather than 751), with UK MEP seats vanishing in October 2010 and any former UK seats apportioned among the other member states being filled by MEPs elected in by-elections in those member states held maybe 3 months prior to October 2010 so that as soon as the UK seats vanished they would take up their seats.
Burnham asks for an extension and it is granted without any rancour.
OR for added drama you could have the initial period ending October 2009 but Burnham asking for an extension after the fallout from the expenses scandal and the Lords referendum.
Nope. Because borders are needed for two reasons (in this case, there are many other reasons for borders of course):
1.
to ensure that customs duties are paid. A customs union removes the need for this because two territories in a customs union have the same customs duties with respect to other countries outside the customs union and they have no customs duties between them on any goods (whether those goods were produced in either of their territories or from outside the customs union). Once this isn't the case, then the possibility exists for trade diversion. For example, say the UK and EU didn't agree to a customs union between NI and the EU, while the rest of the UK left the customs union. And say both the UK and EU have a 10% duty on tractors. This means that legally speaking, American tractors that enter the UK via say Holyhead in Wales, should have the 10% duty charged and if they were subsequently moved to the EU via Dublin they should also be charged the EU's 10% duty. Thus if an importer really intended for the tractors to be sold to customers somewhere in the Republic of Ireland then the cheapest way is to import it directly. Plus customs authorities and governments are gaining the revenue that is due to them. If the UK and EU are not in a customs union though but they have no border in NI and no border checks
somewhere then if say after Brexit the UK decides to drop the tariff on tractors to 2% while the EU maintains a 10% tariff, then a smart importer in the Republic of Ireland (with some creative accounting) would seek to get the tractors landed at Holyhead and pay the 2% tariff and then transport the tractors to NI (from Holyhead directly or via Scotland) and then into the Republic of Ireland. This is now trade diversion as goods now land in the UK (Holyhead) and pay duties (2%) to the UK authorities but end up being used in the EU (somewhere in the Republic of Ireland) having never paid the relevant duties (which go towards the Irish government and EU budgets) and depriving ports in the EU (like Dublin) of trade activity.
2.
to ensure standards are maintained. Similar to 1 above, the EU and UK might have different standards on goods if they are not in the regulatory union of the single market. For example the EU might decide that paint may only contain 2% of a particular chemical which has been linked to cancer, while the UK might decide that based on other research (or the interpretation of results of the same research) that 5% of that chemical is acceptable. As a result, paint containing 5% of chemical X that comes from say Brazil would be allowed into the UK, but would not be permitted into the EU. However with no border between the EU and UK in NI (a sort of gap in the border if you will) then this kind of "Brazilian 5% of X paint" can end up in the EU since no border in Ireland means you can freely import the paint at say Dover, take it to NI and freely move it into the Republic of Ireland from whence it can go to other member states because there would be no checks between the ROI and any other member state.
Again though, the specific circumstances that meant a customs union between the ROI and NI have become unacceptable
to the UK government in OTL (the UK run by the Conservative
and Unionist Party and depending on the Democratic Unionist Party to govern and Theresa May specifically being Prime Minister) don't exist in this TL and so it could well be that Burnham could agree to NI remaining a part of the EU custom union and mirroring the regulations necessary to ensure the absolute free movement of goods between NI and the EU. In this TL, the DUP have 1 MP in Westminster, assuming no change for them between the 2007 and 2008 general election (though they are the largest party in Stormont and are supposed to be power-sharing with Sinn Fein since the 2007 Assembly elections) and the SDLP have 4 MPs (again assuming no change between 2007 and 2008 for them) and the SDLP had had fair relations with the Parliamentary Labour Party which in OTL they attempted to strengthen after the OTL 2005 general election (even accepting the Labour whip informally). The SDLP will likely be very much in favour NI remaining in a customs and regulatory union with the EU. With a majority of 72, Burnham can actually afford to ignore any and all Northern Irish parties, though for internal stability in NI, he is likely to take into account the views of all the Northern Irish parties when crafting the deal with the EU.
It would just fit.