That said,
all of the major parties and some of the most prominent politicians of the time campaigned quite vociferously
against Brexit - though the likes of Boris Johnson did campaign to Leave, as did UKIP (whose raison d'etre is/was leaving the EU).
Once Leave won the referendum, however, things changed. The Prime Minister at the time, David Cameron, resigned. Then, faced with a small majority in Parliament, the next Prime Minister Theresa May called a General Election, where both of the main parties (Conservatives and Labour) vowed to respect the referendum result and formally supported leaving the EU from that point onward. This strategy (famously) back-fired, as May was left without any majority at all and was forced to form a coalition with the Northern Irish Unionists, the DUP.
But... Parliament was left in the awkward position of being composed mainly of MPs who had themselves voted and campaigned to Remain, but whose constituents voted to Leave, and whose official party policy was now to support Brexit.
Subsequently, things got more and more complicated owing to the fact that, unlike a Remain result, a Leave result offered a multitude of options, ranging from an extremely soft form of EU exit (soft Brexit) that would actually leave the UK even more under EU control than it is now, all the way to a 'No Deal' exit, where all EU laws and EU-UK agreements cease to apply overnight. It also became clear (though it was clear to many prior to the referendum) that the EU would not agree to any terms that would leave the UK in a stronger position than it had as an EU member. This (obviously) meant that many of the more optimistic claims and hopes of the Leave campaign quickly became discredited or viewed as 'cherry-picking' - but, paradoxically, this approach by the EU also raised the prospect of the ultimate lose-lose scenario, a No Deal Brexit. (Leave campaigners had, of course, figured this out and realised that the EU would ultimately do what they had to do to avoid a No Deal scenario... but the EU's position was strengthened enormously by the lack of support in Parliament for a No Deal exit.)
Parliament was thus split between a whole bunch of options, none of which could command a majority - until now at least. What happened to change matters was, ironically, the advent of Johnson as PM and the threat of the UK leaving without a deal. The EU played hardball with Theresa May and basically humiliated her at every opportunity. She was left with a Brexit deal that would, in effect, have left the UK in the position of being permanently (and legally) trapped indefinitely inside the EU, but with no voting rights or mechanism to escape. Obviously, this doomed her form of Brexit to failure, and she was forced out. Johnson, however, has played much harder with the EU and basically threatened to walk away unless the EU softened their approach. Fortunately (and in spite of Parliamentary efforts to "take No Deal off the table") it has worked to a large extent, with the dreaded prospect of being trapped inside the EU's legal orbit (via the 'Irish protocol' or 'Backstop' as it was known) now pretty much gone.
The danger now, however, is that although Johnson now has a deal agreed with the EU, and it has (finally) got a Parliamentary majority to back it, too many MPs are still opposed to it for a variety of reasons - some because it is too 'hard' and others because it is not hard enough. Johnson is now taking the same gamble that May took - a General Election in order to strengthen his hand in Parliament. But - like May before him - he could well face the prospect of having to form a coalition again and it could involve the Brexit Party - but most people will be hoping that this doesn't happen, as they would likely reject Johnson's current deal in favour of a far harder form of Brexit or indeed a No Deal Brexit. The EU must be hoping that Johnson wins a clear majority and can deliver the deal as agreed and move on to the next steps, because right now the only thing stopping a No Deal Brexit is a Parliamentary majority against that outcome... but if that goes in December, then the EU may well come to regret making it so difficult to reach a deal that the UK was likely to accept.
@Danoff Not sure that actually answers your question, but never mind