Cranky Flier points out that while tourism to the UK is really a great deal right now (as I'd attest), it's going to be a lot more expensive if Brexit actually happens:
Today the UK is part of the European Common Aviation Area (CAA). That means that UK-based airlines can fly anywhere within Europe they want, just as if they were based in any of those other European countries. The same goes for European airlines flying within the UK. It also means that bilateral agreements negotiated by the EU with third parties outside the EU apply to the UK. And there are a host of European aviation regulations that govern air travel in the UK as well. Some or all of this may go away completely when the break-up occurs. That is to be determined by those negotiating the terms.
...[T]he EU may decide it doesn’t want the UK in the CAA anymore. That would be quite the blow to the UK, but it would be a warning shot for anyone else contemplating the same thing. I keep coming back to that castle scene in Monty Python and the Holy Grail.
That would mean that the UK and the EU would need to set up a more traditional bilateral agreement. It would be shocking if those restrictions didn’t include a ban on UK-based airlines from flying within the EU. That would mean foreign ownership rules would apply. For EU-based airlines this wouldn’t be a huge issue. They’d probably lose the ability to fly domestically within the UK and they couldn’t be majority-owned by a UK shareholder anymore. That’s not really an issue.
For the UK, however, it’s bad news. Think about easyJet, a UK-based airline that criss-crosses the EU all day every day. It would no longer be able to do that. Instead it would be forced to create an EU-based subsidiary, of which it could presumably only own 49 percent, and then have that company handle the intra-EU flying. Half the profits of that company would go into the EU instead of to the UK as they do today. The airline is already investigating this possibility. This wouldn’t hurt easyJet other than adding a little more complexity, but it would hurt the UK.
Yesterday, I thought of a different problem, but related not just to Brexit but to the general British mindset of never wanting to change anything. That problem is Heathrow. It's not fun connecting through Heathrow to go anywhere, mainly because it's only got two runways servicing its five spread-out terminals. Compare that with, say, Amsterdam's Schiphol, or Munich, or even Brussels, and it's difficult to see how Brexit doesn't make Heathrow even less attractive than its continental competitors.
The UK will screw itself by leaving the EU so many ways that porn stars will be flabbergasted. Aviation is just one small area of this.