So what next?
The situation we're in reminds me a bit of the Hitch Hiker's Guide to the Galaxy ... now that we have the answer to the Ultimate Question of Life, the Universe and Everything, we just need to work out what the hell the great question actually was.
The Brexit campaign currently don't have any answers with regards to the issues that people actually thought they were voting on, all we have so far is some back tracking on some of the claims that were made during the campaign .... actually, there is no extra £350 million a week (of course), and actually, even outside the EU we'll probably need to accept free movement of people in order to be part of the single market.
There's only one way forward from here that I can see, and that is a general election. Each party needs to put together their plans for a way forward, and then we can vote for the political party that we believe has the best plan.
Whether they invoke article 50 or not is something that each party can decide for themselves, the referendum has not committed us to leaving the EU. The Lib Dems have already said they would contest a general election based on staying in the EU, and I suspect Labour would do the same. The conservatives will presumably have a pro-Brexit leader by then but who knows?
Tory MP Says No.10 Should Have Had Brexit Plan