They didn't leave yet and may not. I feel like this has been used as a vehicle for Boris Johnson to increase his chances to be prime minister and others' to provoke changes. It seems to me that Britain didn't seriously consider the repercussions of an exit that doesn't involve cherry-picking.
I think this particular Golem has too much momentum now to simply decline the advice of the electorate, however it did occur to me that Cameron's 3 month delay in applying Section 50 would allow the attention of the public to be distracted to some extent.
OTOH, the referendum did kill the Britain-EU agreement on new terms -- as that was expressly conditioned on a "Remain" vote -- so while it doesn't legally obligate the government to withdraw from the EU, in addition to creating a strong public expectation (both in the UK and in the rest of the EU) of withdrawal, it also makes the conditions for staying in the EU worse for the UK than they were before the referendum.
I take the point, and that was a significant part of my own decision to vote remain.
I actually think that the EU itself may scale back the political union bit and push up the economic cooperation bit over the next decade. Then options for the future (on all sides) may open up again.
Those options will be for the ones under 30 now to explore of course and they voted heavily to remain.