Despite calls by pro-Leave Tory MPs for David Cameron to stay on as prime minister, it is difficult to see the man who called the referendum in the expectation of an easy Remain victory and went on to lose it remaining in post for long.
Chancellor George Osborne is also expected to resign in the wake of the referendum result.
It is not clear how quickly negotiations for Britain’s exit form the EU will get under way. Mr Cameron had indicated that in the event of a Leave vote he would immediately invoke Article 50 of the Lisbon Treaty which allows countries two years to negotiate a withdrawal agreement.
But Brexit campaigners have suggested there could be less formal talks before starting the official process.
However it is done, the chances are that the other 27 EU nations will not be keen to give the UK an easy ride. They have no wish to encourage anti-EU forces elsewhere.
Negotiations may be led for the UK by a new Tory prime minister, if Mr Cameron resigns. Boris Johnson is the favourite to take on the job, though Theresa May and Michael Gove are also contenders.
The referendum has already seen the pound fall to its lowest rate since 1985 and there are likely to be further serious economic consequences.
It is possible that in order to try to stem the fall in sterling, the Bank of England will put up interest rates – at least in the short term. This would have a very “real world” effect, as it would mean the cost of mortgages and borrowing would immediately rise.
But the Leave decision could also spark a constitutional crisis. The result showed a stark division within the UK. Scotland’s strong pro-Remain creates exactly the scenario Nicola Sturgeon and the SNP warned of - Scotland being dragged out of the EU against its will. The Nationalists said this was the kind of issue which could trigger a second independence referendum and now there will be many pushing for just such a move.
Ms Sturgeon will still not wish to risk another independence vote unless she is sure she will win it, but the Brexit vote may well stir up enough outrage among Scots to make a majority believe independence is now a better option.