Just my 2 cents , tough I don not live in UK it affects me as well.
Unfortunately, the bureaucrats in Bruxelles can't dictate anything, look at Poland or Hungary who destroyed their justice systems, EU is foaming at the mouth but really it is nothing they can do about it, Hungary PM is negotiating back deals with Putin with no worries.
UK, like any other country had the Veto right on all important things, exercised by your elected PM, plus all the opt outs they negotiated at the entry, like non Schengen, no euro etc. Nobody forced UK in to anything.
At work I have colleagues from an international background, from all over, and after the initial shock in 2016, now most of them are a bit amazed and amused at what is going on now with the MP's and Theresa May.
Nobody will shed a tear for BMW selling less cars in UK, they are expensive anyway and who buys them they will afford the extra 10 % or what ever the tariff will be. The impression is that as long the UK decides what it wants, the EU will negotiate in good faith, but here people had enough of this circus and in the EU we need to move on to more important debates, and a lot of people hope that this will not be prolonged any more.
Don't get me wrong, I have all the sympathies for UK, it is a big loss for the EU, I think a lot of lies have been told by the leave campaign, but also a lot of people have been left behind not only in the UK but in all Europe by the financial crisis and globalization, and leavers have very valid points about a democratic deficit in the EU project and for sure a lot things can be improved.
And the worst of it all, the biggest mistake done all over Europe, including UK and US, nobody paid for the crisis we had it by doing time or loosing money but the tax payer. The richer got more rich and the poor and middle class got left behind. And this anger now it is showing in lot of votes, not only in the UK but all over.
Will the populist provide a solution ? Time will tell. In Italy, the only country where they are in power, they did nothing significant but bark at EU with a lot of noise and than business as usual.. kept the huge italian bureaucracy there in place 0 public investment.. economy down the drain.
In the case of UK, EU was an easy target to blame for anything, like it is happening all over. If not EU it would have been the the Bank of Japan, China, the Free Masons, just about anything except the people at the top.
Your thinking that EU will make concession is very optimistic. UK last month got blocked in WTO by Chile, and UK does not even have a preliminary talk with any other country in the World, and it has been almost 3 years..
Don't worry, it will take a miracle and some very serious commitments from UK to get an extension beyond June, no matter what your parliament or PM decides. Unless of course you guys change your mind

and stay in after all.
It will be your choice as a country on what kind of relationship you want to have with EU after, I hope it works out well, but by the looks of it.... you will probably get your hard brexit or none.
I hope I did not offend anyone, it was not my intention.