To leave the EU a nation, such as England, is to invoke Article 50. This is the clause that allows a nation a pathway to leave the EU. My understanding of Article 50, limited as it is, suggests this is mostly window dressing as it does not in fact define an actual pathway.
Upon invoking Article 50 the EU and the nation begin negotiating the terms of the exit. This is key because it means how the exit happens is as yet undefined. The EU will undoubtedly make the terms less then pleasant for the exiting nation. They will also create a long term process of negotiation to chew up the clock as much as possible. If at the end of the first two year period the exit is not in fact fully negotiated and executed, the 2 year period can be extended as needed. This can in fact be a never ending process or one so unfavorable the nation won’t wish to take it.
A nation can reject the authority of the EU and stop cooperating during this exit process. However its probable that doing so will subject them to any number of penalties as part of their existing membership in the treaties that make up the EU. A nation attempting to ignore the EU on this will encounter a focused headwind.
Ultimately the EU’s path will likely be the same as they ran with Greece. They will drag it out, make it unpleasant, and try to cause pain for England that is associated with the exit in the hopes it displaces the upstart political movement attempting to exit. If they can succeed at that then the exit can be reversed and the union preserved.
To let England successfully leave is to leave the EU toothless. Other nations would then believe it is possible to leave any time they felt like. That would make the EU a paper tiger. Every possible leverage point will be utilized to make sure England, despite this vote, doesn’t actually leave.
Ultimately you can checkout any time you like but you can never leave.