- Scotland is likely to go (despite what the polls say right now)
- Northern Ireland is quite likely to join Ireland
- God knows what Wales is going to do
It looks like the Cymraeg [language] loving Welsh-nationalists are likely to press for all schools to become Cymraeg language and demand all businesses to move that way too. That should push taxation to new levels, reduce school achievement further, and retard international businesses from entering/remaining in Wales.
Given the North-South divide in Wales (even amongst Cymraeg speakers) I'd expect the massive demographic differences to push it back to the pre-annexation days where Gwynedd in the North was the central power (due to Irish/Viking immigrants after the Roman exit AFAICT!). Cymraeg speakers in the low-population North will break away and enter an economy propped up by tourism. The South-East is 90% English speaking, has three-quarters of the population and relies on the M4 corridor for a lot of its economy it's staying close to England one way or another.
In short Wales is already starting to pull itself apart. The low-income Welsh people who benefited a lot from EU schemes [eg in The Valleys (S.E.)] voted to Leave though, I don't think they'd try to follow Scotland back to the EU. However there's still an undercurrent of "we were conquered by the English and will hate them forever".
An oft-overlooked factor that interests me is the Crown - what have they got to say about it all. I assume they're keeping their beaks out to ensure they keep Crown money and property but along with all of this it strikes me if they aren't going to retain a political union of "their" lands then there's no longer a regent in even the hands-off sense we have in the UK today.
Why you'd throw off rule of the Queen's government and choose to stay being Her subject is beyond me.
So, I don't think it is as simple as: 'Northern Ireland is quite likely to join Ireland'.
I sort of wish that were the case. The reality is likely to be a lot more problematic than "quite likely", and has every danger of becoming quite violent, to boot.
But any kind of devolution for London that makes much difference will end up increasing divisions, and increase the odds the UK fractures further. I have a hard time picturing a UK 30 years from now without imagining a Westminster that has devolved away most of its powers.
Even then, I suspect Scotland will still leave sooner or later, and possibly Northern Ireland too.
Much more likely, though, is that everyone argues about it for decades and nothing happens.