Until now I have thought it would be a horrible abnegation of the first referendum to have a second one. I still think so. If a country makes a decision, it ought to be final, or whichever side loses will always demand a second one.
Unfortunately, Brexit may reasonably be perceived as a spectrum decision, not a binary one. There are different elements to the EU. For some of them, people may believe the benefits outweigh the costs. For others, the opposite.
I have been thinking about a solution to Brexit along these lines. Not one but two referenda. A second referendum, in which new questions are asked about the elements of the EU in which people wish to remain/leave, with a third referendum taking place ten years after the second one to review any remaining elements of EU membership after the second one. Once we leave any part of the EU, we are fully out. This way, both remainers and leavers would have a potential benefit from these two referenda.
The politicians are likely not in a position to figure out a solution themselves, as they are organised along economic/political lines, not theories of sovereignty.
So sadly, I think the people will have to take the decisions for them, again.
The second and third referenda would pose three or four binary questions, assuming that the UK has expressed an interest in at least a minimal Brexit, which is to say that the desire to retain the UK's sovereignty is decided and we will go no further towards a federal Europe. The queen is our sovereign; the UK parliament is our model of government and retains ultimate authority; and the UK courts are the ultimate legal authority in the UK.
Here are the questions.
1. Do people wish to remain in the European customs union or have their own borders?
2. Do people wish to leave/remain in an agricultural and fisheries union?
3. Do people wish to leave/remain in a common market for goods and energy?
4. Do people wish to leave/remain in a common market for services?
Something along these lines.
This would give the politicians the roadmap they clearly need.
If they know what is demanded by the British people, they will have something to work with. Instead of assuming they know where Brexit belongs on the political spectrum. And what parts of the EU they continue to wish to belong to it.
Also, it avoids the issue of a General Election which would also decide things which have nothing to do with Brexit.