Having followed the proceedings in the Untied Kingdom of the past few day from a bit of a distance, let me be impudent enough to offer some (unedited) points (*ahem*)
(Warning: lot of text ahead!)
1) I don’t know how the rules and procedures in the UK with regard to organising referenda and following up on its outcome are, but I will assume things went according to the rules, and the results FOR Brexit, with 52/48, stand.
2) But I very much doubt these results mean something like ‘52% wants out, 48% want to remain in’ in black and white. Whilst a considerable number of people may be all-IN or all-OUT, I believe that a part, possibly a (vast) majority have had severe doubts about either staying in and accepting the way the EU is run (at the moment) with all possible doubt and hesitation, or getting out from under the EU’s workings and try going by itself, with all the cons that may have. In short, may have felt they have had to choose between two bad choices, and have been wavering which one was the least bad thing. The 52/48 may thus signify for many the fact that getting out sounded just ever so slightly less bad then remaining in.
3) It seems clear that such doubts about the functioning of the EU at present are confirmed by the behaviour of the EU government, headed by Hauptmann Juncker, whose reaction that the UK should now leave the EU at the soonest inconvenience, and that the separation need not be smoothed in any way whatsoever (‘for the marriage was never a happy one’)something which says a lot about). Such indicates not just a rather scary disdain for a democratic process in a member country, but also seems to run rather ahead of things, for before any talk can begin about the separation, the UK government first has to formally accept the outcome as decisive (the referendum was consultative, therefor not binding), and then, if they accept the outcome, start the Article 50 procedure. And only then can there be any talk about how things are to proceed. But the initiative lies with the UK, and very much not the EU council, or Juncker, or anyone else in Brussels.
4) To add to that, one might well ask the question as to why the EU council now goes all bezerk about the processes in the UK, when it presently, and completely against its own rules, is pumping any amount of money into a country that has been lying to the EU for a decade, rather than kicking it out. Bailing out a irreparably corrupt country (correction: making sure some shifty banks, guess who might be shareholders there, who lend the money against impossible interest) with taxpayers money is OK, but a free democratic process is very much not? Such is not exactly building trust in the powers that be, no?
5) What seems also clear is that politicians in the UK at large, with but a few exceptions, have utterly failed to give any sensible, fact-based account about what would be the benefits of a Brexit, and what the drawbacks. Rather, sides seem to have drawn rather apocalyptical pictures, that the UK would invoke Ragnarök and Armageddon when going out, or drawn empyrean pictures about how the UK would float to Valhalla itself when separated from the stygian mire that is Europe. What they should have done is explain that the UK may be an independent country, but that for its sustenance it is very dependent on its various connections with the EU, ties that have become all the more intricate in all the years it has been part of the EU, and that unravelling them will have possible positive consequences, but also adverse ones.
6) The UK politicians have failed to give an answer to some very basic questions, and it would appear they failed to give that answer because they haven’t thought about it yet. Such as:
a. A lot of UK laws are based on EU regulations, which the UK inserted in their juridical system. If the UK bails out, all these laws, all of a sudden, become void. Does the UK fall back on previous (pre-EU) versions of these laws? Does it need to make these laws anew?
b. There are some 3 million EU citizens in the UK, travelled there without passports because of Schengen. These 3 millions are, suddenly, illegal in the UK. What to do with them?
c. Likewise, there are 1,2 million UK citizens living within the EU; they are suddenly illegal too; what to do with them?
d. Trade. All agreements about buying, selling and traffic are off. The UK will need to negotiate new ones, while all benefits (such as subsidies for farmers) are gone, and with the Russian ‘blockade’, trade within the EU and without the UK isn’t all that booming at the moment, so not getting any farm goods from the UK on the EU market might be a boost for the EU market. But not for the UK market, which will implode.
e. The Pound will devaluate considerably (it already has), which will mean it will be far more expensive for the UK to buy from the EU, which it will not be able to avoid. This may lead to a cascade in which the UK will have an increasingly worthless coin to buy increasingly expensive stuff from the EU. In other words, a skyrocketing inflation.
f. The EU members will have a considerable diminished interest in letting the UK partake in any deciding developments with regard to the future course of the EU. With the UK needing the EU (with all its deficiencies) far more than the EU needing the UK, the UK will start to drift behind, with little or no influence on matters.
7) The UK leaders, especially the ones campaigning in favour of the Brexit now all of a sudden seem to be running away from the responsibility they hold. The behaviour of Boris Johnson may be a showcase in this. After vigorously campaigning for the Brexit, it seems that he now has been scared to death by the result. For not only was his first speech after the results came in to be one of someone who is trying to crawl back and pretty much undo the result (‘we have no haste’), but after that he vanished. It seems he has been mainly campaigning with the intention of presenting himself as a ‘Brit for the Brittish’ without ever thinking he might get 52% of the voters, but rather was certain the UK would vote ‘remain’, and then use that ‘buy Brittish’ image in the next elections to play the populace. Now, all of a sudden, he has to take up what he helped engender. A bit like a priest leading a, rather overheated, praying session invoking the answer of the Lord, and then suddenly sees the roof being ripped off by a might hand and hearing “All RIGHT THEN, YOU HORRIBLE LITTLE TWURP, WHAT DO YOU WANT FROM ME?”

Neither political side seem to have made any plans whatsoever about what was to happen when the vote would be ‘out’. No ideas as to what is to be done, let alone how, let alone how with the least bit of damage. This means the EU will be in the lead, to the considerable deficit and damage of the UK. More precisely, to the people living in the UK, who will pay a hefty price.
9) The difference between Scotland and England has been set more pronounced, and the UK may come to face the decision whether it is one country, or just a, rather loose, alliance of two different ones. If it finds itself to be two rather than ine, yet another separation, with all its costs may be in the making. If Scotland does split off, and rejoins the EU, England will find itself isolated even more, and this time even deeper, for the closer partners have been before, the more alienated they will be after.
10) However, perhaps, even if the UK leaves the EU, the very fact that the sentiments (or rather; doubts about and resentments against the EU that are very much and increasingly churning in the EU about the EU, especially in countries – not least my own - that operate above the political/social/financial mean gross average of the EU, which in some respects is pretty mean and gross) have come so very undeniably into focus, may come to make that the EU takes note and changes course. The EU was once started with idea of increased cooperation between various states within Europe, to the betterment and benefit of its people living within these member states. But rather than advancing along that course, and letting new members states in when these candidates had reached the level needed to enter on the same level as the existing members, it has become the hostage of an utterly unrealistic attempt to force at the greatest speed possible all countries within Europe, especially those within the former Eastern Bloc, without checking if these countries were ‘fit’ to enter. A forced multiple marriage of convenience, rather than any sensible arrangement. With all negative repercussions to follow; it’s not the first time someone has tried to force Europe into one (the last attempt was sometime last century), but such attempts have not only never been successful, but rather have driven countries away from each other. Rifts taking decades if not centuries to close again.
As to the Brexit enthusiasts, let me state clearly that I have any amount of doubts as to how the EU is currently run, and increasingly so. But I fear the UK has more to lose from a Brexit than to gain. The UK getting out of the EU may well mean it is burning its ships behind it, which is never wise, but certainly not when you live upon an island. And I do wonder how many Brexit-voters will come to regret their vote, once they learn what the price is they will have to pay, once the British Pound will be reduced to the English Ounce. I wish them well!....

(I note they're pushing againt my country. Oh well, wouldn't be the first time. But do note England once had a Dutch king, but The Netherlands never an English queen!)
All best,
gep