The Brexit camps idea that they could leave so they could finally pick whatever they like, as they have been trying to do for the last 40 years, is cute but laughably naive. They will not continue to receive the free travel, trade access and EU subsidies to the tune of 200 million euro per week. All of that will be revoked, only if to set an example that you will not get those benefits without buy-in.
In my view, there are currently two equally likely scenarios to unfold: they leave with nothing as farewell gift (as has already been hinted at by the EU), or they will ignore the vote and stay in because they realize how bad of an idea this was - but are now in such a bad position they will likely lose all special privileges they enjoyed over the last 40 years.
This can be clearly seen by how many leave-voters are now in shock that they leave, and want to be able to vote again to remain. This was a powerplay for a better negotiation position. It backfired and now they can eat it.