Vernon Bogdanor, a professor of political history often on the BBC to talk about aspects of the constitutional law gave a speech in June to Gresham College in which he outlined his thinking on Brexit (HERE). He is an advisor to governments and the closest thing we have to Henry Kissinger. The speech is interesting because in it he concludes the so-called soft Brexit where we join the EEA is, as the Brexiteers have always claimed, membership of the EU in all but name. If it came to the choice of the EEA or the EU he says we may as well remain in and at least be able to influence the rules or veto stuff we didn't like.
So he effectively says the choice is between a hard Brexit and remaining in the EU and he thinks the 2017 election effectively reopened the question since Mrs May did not get the majority she wanted which would have meant an end to all possible arguments. He also says the new House of Commons is even more pro European than the old one and the Lords are newly emboldened because of the Salisbury rule where they accept laws being passed without real challenge only if they were in the ruling party's manifesto and they got a majority at the election.
He also thinks we are in a weak bargaining position with the EU as we have always thought. He quotes Mrs May from a speech six weeks before the referendum:
"The reality is that we do not know on what terms we would win access to the single market. We do know that in a negotiation we would have to make concessions in order to access it; these concessions could well be about accepting EU regulations over which we would have no say, making financial contributions just as we do now, accepting free movement rules just as we do now or quite possibly all three combined. It is not clear why other member states would give Britain a better deal than they themselves enjoy".
One further point is that he makes a distinction in the EU between a free trade area, the customs union and the single market, which I never heard made before but I am sure he is right. The old EEC was a free trade area but it was not until 1992 or so that the single market was created.