So you voted in favor of a fundamental and permanent constitutional change that will take away the European citizenship and the rights that comes with that from your fellow British citizens because it could, possibly, perhaps, eventually, lead to a left wing government? Wow. And you don't care about anybody else's economic circumstances as long as you are doing fine? For somebody who wants a left wing government in power you seem to have glossed over a quite significant part of what left wing politics is all about.
You get 0/10 on your logic, but a solid 7/10 for being an interesting fella'.
My prediction (or perhaps more accurately, fantasy), though, would be that Brexit will be the downfall of the left-wing socialist Left in the UK, and the catalyst for the rise of the center-left liberal Left. In my mind it goes something like this:
The economy goes into a recession by 2020, regardless of Brexit, the UK leaves the Single Market and Customs Union on December 31st 2020 as the transitional agreement ends, worsening a recession that would've happened anyway but getting all the blame. The finance industry of the City crashes as part of the industry heads for the continent out of necessity after losing passporting rights etc, taking with them a substantial amount of the UK's GDP. The SNP uses the economic turmoil to their advantage, and secures a victorious #IndyRef2 and re-joins the Single Market (but keeps out of the EU itself, aka 'Norway option', to satisfy the Eurosceptic rural fishing industry). The economic uncertainty of Scexit further harms the UK economy, the pound takes another hit. The Tories gets blamed for tanking the economy and breaking up not one, but two unions, the European and the British. By the time the elections of 2022 occurs, Jeremy Corbyn has transformed the Labour Party to a point where we might as well re-name it the Corbynista. The Corbynista easily wins the election, securing a massive enough parliamentary majority that no pockets of resistance within the Labour Party Corbynista has any sway whatsoever. The Corbynista begins to nationalize key industries, the pound tanks and loses its status as a reserve currency, while the City takes another hit as firms active on the international markets opt for New York City over London in this new business environment. Continued economic turmoil means that Irish Republicans sense their moment, and Jeremy Corbyn refuses to speak out against an Irish Unification referendum, something he has long supported, opting to stay "neutral", in a way that comes across to everybody with half a brain that he in fact encourages and welcomes Irish Unification. The UK breaks up again, Northern Ireland re-joins the European Union as a part of the Republic of Ireland. The Venezuelan economic policies of the Labour Party Corbynista does not go over well in an economy so dependent on services and so tightly integrated with the world economy. By the mid 2020's it is clear that this will be a lost decade for the UK, with people already having emigrated for job opportunities and higher wages elsewhere, due to years of a falling economy and currency, with Australia and New Zealand especially feeling the influx of Brits, but Canada, the United States and the European Union seeing substantial inflows as well.
With both the major parties having destroyed the economy and broken up the union in their own ways, the ground is fertile for a new progressive force to grow. Along comes a coalition of minor parties led by the Liberal Democrats that merges into a new political party called the "Progressive Liberal Party". This new center-left social-liberal party wins a landslide as voters turns to the center on promises of restoring the UK's fortune by rejoining the Single Market. Just as the economy was starting to turn around anyway, the UK re-joins the Single Market, which then of course gets 100% of the credit, far more credit than it derserves even though over time its effects is positive for the UK economy and that of Europe as a whole. The importance of the Single Market is now unquestionable in British political discourse on the one hand, on the other memory is short. As such, the left-wing Labour Party Corbynista is what most people will remember and associate with this era at this point, not the failures of David Cameron or Theresa May. The moderating, pro-European forces within the Conservative Party has long been gaining ground and now takes full control of the party, which becomes he main opposition as a center-right party, while the Labour Party Corbynista is all but obliterated from the political scene just as UKIP was years ago by now (Nigel Farage emigrated to the Falkland Islands years ago, where he has begun a campaign to restore 19th century British society on these islands through his new party, the Falkland Islands Independence Party, or FIIP).
So, ultimately, my long-term prediction wild fantasy is the opposite of what you wanted, the destruction of the left-wing in the UK (and the right-wing).