Yes, they do, their plan is to re-assert border controls and negotiate the best deal with the EU possible from that starting point.They can't reassert border controls while negotiating to be part of the common market, and they need the EU far more than the EU needs them. The leave campaign plans were fantasies sold to the electorate, and some frankly very distorted (like 350m for the NHS every week), and they have rowed back on almost all their promises. So yes I think it's fair to say they don't know what they're doing and certainly to say that they have no viable plan. Here is Boris Johnson traducing everything he stood for on the campaign trail in an attempt to court Brussels and the rest of the electorate (attempting for example to claim that the campaign wasn't about immigration after all):
http://www.telegraph.co.uk/news/2016/06/26/i-cannot-stress-t...
and being soundly rebuffed the day after:
http://www.theguardian.com/politics/2016/jun/27/brussels-rej...
If they reassert border controls UK trade would suffer massively, they simply can't take that risk, and if you read what the chief architects of the leave campaign are now saying, it's clear they know this and are going to have to compromise massively on their promises, including not imposing border controls at all, because that wasn't a very practical idea, and it would lock them out of the EEA.
What makes this guy think the EU will actually even exist five years from now, let alone be something actually desirable to be a part of?
Many people now feel the same about the UK, the markets are certainly behaving as if the UK is damaged goods. Ask citizens in Scotland, Gibraltar, London or Northern Ireland and you'll find they're being taken out of the EU without their consent - all these regions voted to remain, only England and Wales wanted to leave. There is a serious possibility of the UK not existing within 2 years as Scotland wants a referendum. Perhaps Brexit will mean the downfall of the EU, which you apparently consider with relish, but I doubt it, and sincerely hope not, as that would mean almost inevitable war on the continent. I suspect the EU will survive, as long as they can stop petty national concerns (like German domestic politics) from interfering in their treatment of important issues like Greece.
While this London petition was obviously born of frustration and isn't particularly helpful, it does raise an interesting issue - many inhabitants of cities nowadays don't feel any particular allegiance to a given nation state or regime, nor do they want to, the reason they voted remain is simply to keep parochial identity politics out of their lives, and be part of something bigger. I think the really interesting issue here is how nation states and national identities are starting to be blur (they are after all relatively recent invention), and what will replace them as globalisation spreads.