I'm a bit late to this thread. I had to make a trip by road (not on the bike, unfortunately) to Lithuania the day after the result was announced. I had gone to bed confident that the Remain camp would win, so I was shocked to hear that the Leavers had won. I wouldn't say they won the argument because they didn't put forward any coherent argument, just a lot of rhetoric and slogans about sovereignty and immigration. A major problem is that the arguments for and against membership are far too complicated for the average person to understand, so they voted out of fear and emotions whipped up by some sections of the press and politicians who thought they could benefit from leaving the EU. I was and still am of the opinion that it would be much better to stay in and use the support of other member states which also have populations who feel that the EU isn't acting in their best interests (e.g. France, the Netherlands, Denmark, Poland) to put pressure on the Commission to change its ways and become less autocratic.
What many don't seem to realise is that without the EU employment regulations, the employers will have a much freer hand to reduce pay and holidays, increase working hours and generally do whatever they want to reduce costs to compete with China.
On my trip through Germany and Poland to Lithuania people seemed genuinely sad about the Leave vote, and I don't think it was just because they want our money, as some had suggested. Our group felt that we had to try to explain to anyone who would listen that the decision wasn't what we wanted. It has been said many times that the referendum isn't binding, but I think the more vocal Leavers would do their best to stir up as much trouble as they could if we stay in. My hope now is that the government can do some sort of deal which ensures that we retain as many of the benefits of membership as possible. Alternatively, the EU as we know it may fall apart and be replaced in due course by a new alliance without the political aspirations of the EU and without the ridiculous level of bureaucracy and waste that I have always disliked.
It was a big mistake to go ahead with the referendum without the necessity for a convincing majority vote. A 52/48 vote isn't enough to take such a huge step, a 60% or even 65% majority should have been required because it is a much bigger decision than simply changing government.
One thing that nobody seems to be talking about is what might happen if Trump becomes the US president. He is on record as saying that he can't see why America is in NATO and Europe should look after itself. If the EU is in crisis and he pulls America out of NATO, who thinks that Putin (who has spoken admiringly about Trump) could resist the temptation to finish what he started in Ukraine, and even reclaim much of the former USSR territories lost when Communism collapsed? His pretext could be the same as he has used previously, the 'defence of Russian minorities'. Where would he stop?