Ok...
First off, Quebec is a bad analogy for this. It's not a great one for Scotland, since that at least was a real country in the past and had viable plans for the future, but it generally fits there since they're both provinces of a federation wanting to become sovereign nations. Here, you have a sovereign nation withdrawing from a strong common market and bureaucracy. And one which has historically had some pretty noticable differences from the rest of them.
But, to go point by point. We've already covered why Cameron can't just go "Nope, doesn't count." Heck, let's toss in a third one. PArt of his mandate for this term was that he would run this referendum. To ignore the results would, again, undermine his credibility. Something else that Cretien didn't have against him, since he was pretty generally of the opinion that the Quebec Referendum was low on credibility to start with, but he'd humour them and win anyways.
Some businesses are going to up and move, but mostly just the Europe focused ones. Anything focused specifically on England and anywhere not Europe will want to stay in England. Also, the reason for leaving Quebec wasn't just the instability. You have to remember, the reason Montreal used to be The City in Canada was because when we got our first real hit of settlers, Montreal, Halifax, and Quebec City were the only real places to go. Halifax was too far out of the way, and Quebec City was too French, so Montreal. This meant that a lot of the business there wasn't French. The reason it moved to Toronto was because Toronto was rising as competition to Montreal, and because the nationalist movement in Quebec was Francophone in nature, and thus anti-Anglophone. Basically, they left because the political climate was poisoned and would get much worse if Quebec did separate. English business, based in England, which left the EU in order to promote English causes, will find their situation to be the exact opposite of Anglophone business in Quebec.
Hmm, Scotland. Yeah, probably will leave. Dunno about Ireland, will be interesting to watch. Not expecting huge waves of immigration though. That feels like the BS claims that we should expect waves of immigration whenever a Republican wins the White House and yet they never materialize. The mention of the United Empire Loyalists is interesting, but not really applicable. First off, I really doubt many people feel that much loyalty to the EU. Secondly, a lot of the UELs were refugees. Seriously, as far as the Revolutionary War went, it was effectively a civil war, and a lot of the UELs were having homes burnt down, tarred and feathered, shit like that. So, yeah. I'll believe in major population shifts when I see it and not a moment before.
As for the stock exchange. I imagine Germany or the Netherlands probably will try and use this as an excuse to make their own. If the EU remains powerful enough in the long run, it may one day supplant the LSE. But that won't happen overnight either.
As for the monarchy leaving. They weren't driven out by the blitz, they're sure as hell not going to leave because Britain left the EU. MC, this one is straight up "I hope they suffer for doing something I think was dumb" wishful thinking on your part.