It's unclear. No one knows. One of the main drivers of the Leave vote seems to have been immigration. Currently, the Irish border is nearly invisible. Do you not think that the UK's only land border, which it shares with the EU, will necessarily have to become more real if the will of the voters is to be kept?
That is the nature of national sovereignty Rex, the UK is under no obligation to acquiesce to the mass immigration which impacts jobs & places to live, over-regulation and adherence to EU laws, and financial drain to a bloated bureaucracy like the EU is imposing on them. The UK is the 5th largest economy in the world and they will be able to stand on their own quite well without the EU, there really is no value added for them to stay in at this point really. Time will tell but, I suspect the EU is getting ready to implode and the UK will define their borders and the rest of the stakeholders (Ireland, Scotland,et al.) will also have to make decisions whether they want to stay with the UK or bond with the EU but, that might be a short lived decision to hitch their wagon to the EU...France along with four other nations are thinking of leaving the EU as well.