Once Boris / Gove / May(?) is made PM, I wonder if they'll delay acting on Article 50. It seems likely that to actually serve notice will finish their political career.
Once Article 50 is activated, there needs to be a huge increase in the size of the civil service (the un-elected bits of government that people don't like). We need to re-issue passports, create visas and grant them retrospectively to foreign workers already here. The paperwork for ex-pats to be able to stay in the countries they are in needs to be formalised. The trade negotiations for deals across the world will start. A tiny piece of work is drawing up the new immigration policy - if there is any time for this. A good chunk of the money we are currently giving the EU will go to expand the civil service to pay for all the people that'll be needed for this work while the new government is busy with the increased day to day business for all the new and amended laws we have to enact before we exit. I hope no-one is expecting much of the money to be used to pay for the things currently subsidised by the EU or to help the NHS. You can't spend it twice.
As the leave campaign have already said, exit will have almost no effect on immigration. There will be many "unfortunate incidents" related to this. I can only see two alternatives for the next leader. Embrace the right wing in toto and whip up the xenophobia or retire and take away the dreams of the leavers. Not much of a choice.
I can see the next PM delaying this decision until the next GE. The uncertainty is likely to affect everything negatively. Cameron stitched them up big time by resigning without starting the Article 50 process.