1. The vote said Leave the EU, it said nothing about the CU or SM.
2. Not one of the Leave campaigns said we would have no deal. They all promised the easiest, cake and eat it deal in history. However, Parl should never have countenanced a referendum which it couldn't enact. As a deal required the consent of the EU as well as parl, there was no way a vote could specify any deal, unless the EU and the UK had agreed the future arrangements before the vote.
So we are, in effect, enacting the vote which was a choice between Remain and whatever deal the UK PM returns with which commands the support of Parl.
We should have had a remain vs no deal vote 2-3 years ago. Given we didn't we should have one now. Have May's deal (and Norway, too, if you want) on the first ballot and then use 2nd and 3rd prefs to get a winner.
The only possible argument against this is from Brexiters who haven't changed their mind, and don't think others should be allowed to. Or Brexiters who wanted no deal when they vote leave and therefore think everyone else should have done.
Speaking generally, I think the below lists the things we like and dislike as a country.
Like
Customs Union/Free trade/Single market
Visa-less travel
Dislike
Free movement of people
Having to give lots of money to the likes of Greece and Ireland
Being told by Brussels what to do
Sort of, but not exactly. We have no problem with foreign folk coming over for a holiday, spending some money & then returned from whence they came. We do have a problem with foreign folk coming here to settle.
We do not ask for the right to settle within the EU. What we ask is that we can still visit Tuscany/Bordeaux/Corsica etc without having to go through the palava of obtaining a visa.