Brexit was undefined before the referendum. People didn't know what they were voting for. So we should be permitted to vote again if we are happy or not with the result. Consider the scenario of a hard Brexit, no negotiating power, and no trade deals, and the pound falling. Re-joining the EU may be the best option rather than forging our own, very expensive and very costly venture.
We voted once. We voted to leave. The European Union are now holding us hostage. More people want to leave now than before, so how about we do so? Right now. We should cut off our nose to spite the EU and then get a better whole-world-sized nose. If the left lose this second referendum, will they ask for a third? Probably. We brought democracy to our empire, and it seems as though we've left it behind with us.