Czechoslovakia split in two with minimal rancor and no violence. The breakup of Yugoslavia resulted in a ghastly war. Brexit will fall somewhere between those two poles; the point is that the secession process can be whatever the parties decide it should be.
My best guess is that the process will be nasty, brutish, and long (in a diplomatic way), for the following reasons:
1. The British government is wobbly, and doesn’t really know what it wants: Should the 2017 election be viewed as a mandate for a soft Brexit? I can’t tell; neither can the government.
2. The EU’s position is a lowest common denominator, and it’s unreasonable: Getting everyone on board with a negotiating strategy means giving every member what it wants, which is likely to cause major conflicts during the negotiations.
3. The matter is very complicated, from a legal perspective: It may well be that splitting a sovereign nation into two parts is legally simpler than seceding from the EU.
The process is likely to take more than two years. As it becomes more and more obvious that the interim “solution” will be the default WTO trade relationship, the trickle of multi-national businesses moving to the continent will become a flood. The pound will plunge, growth will stall, and things will start getting really ugly in the UK.