The remainder will then follow bit by bit with England likely last.
If the UK manages to hold together then it will be welcome to return but without the special exceptions that were made for it in the past. The good deal they had was squandered and the negotiation position of the EU has strengthened accordingly.
Alternatively, the UK could conceivably try to get closer to the USA (not physically, obviously), but I doubt that would fly given the distance involved.
The funny thing (well, not really funny, but given the situation there is something that borders on humor) to me is that England is absolutely adamant that Scotland can't secede from the Union when that is exactly what they just forced Scotland to be a part of with the EU. It boggles the mind how they twist themselves into the weirdest illogical pretzels arguing that when Scotland voted to stay in the Union that vote was binding even post Brexit, as if the circumstances haven't materially changed.
We'll see how that one ends.
But eventually the only thing that matters is the economy and for now that doesn't look all that good for the UK, the sooner they turn around the better for everybody. But Europe is not going to push for this, it will have to come from inside for it to work.
Also, I think the idea that all that matters is the economy is glib nonsense. Whether people should vote with their emotions matters little, when they in fact do vote with their hearts. My own feelings on Scottish independence aside, I wonder if the Scottish Nationalists would have had more success in the last referendum if instead of making an (IMO rather weak) economic argument, they had stuck with the more emotional case for independence. "Yes, voting for separation from the UK will make us poorer for a time, but it'll be worth it to <sound of trumpets> be free."
I am from a place that impoverished itself for most of a century via independence, but I don't think many of us would vote to back with our old imperial masters now.
Nationalist sentiments ('free') are obviously going to have to take a backseat to those. So I don't see how a referendum on that using the dual theme of being 'free' and then immediately joining the EU would work in practice, that sounds like arguing both sides at the same time.
In the EU nobody cares if you make bad political decisions at the local level, like in Poland or Hungary, but once you create 4 years of painful Brexit negotiations for all other countries involved, then people care about you wasting their time.
But Scotland and Ireland don't really benefit from 'The City' and as such lost a lot more than they gained. These side effects, conveniently ignored by the 'leave' camp come with a major cost attached, which will likely negate all of the gains.
And then there are still the questions of internal borders, Schengen and the Euro.
I don't have a cite for this, but I think I read somewhere that Spain has said they will have no objection to Scotland joining the EU as long as the separation of Scotland from the UK is done legally under UK law.
And I mean full, not just the road speeds but also beer served in 250ml, 500ml measures.
Scientifically, the majority of drivers drive better on the left too, due to dominant right eye.
As a EU citizen who likes the EU, I think the EU has a lot to fix and I hoped that Brexit would be a wakeup call for the elites to get started. But it doesn't look that way. The fact that von der Leyen is President of the EU commission is a clear indicator for what is currently wrong with the EU.
Overall, I would say that some form of participation in the EEA is more likely. Something that a government could sell to the Brexit voters with a reasonable amount of fudge.
I don't see the UK being "welcomed back in" any time soon. I see the UK being allowed to align rules with the EU, i.e. economic openness, enjoying the benefits of alignment, but not full membership and a vote on on serious matters with the core EU members. Maybe a decade or two later that would happen.