How would it be any more of a muddle than when anything else in legislation changes on a particular date?if a country deciding to leave refused to agree arrangements for leaving, for example what date they would quit their offices, what date they would stop attending Parliament, what date they would stop receiving subsidies, what date they would stop paying contributions, what date they would stop having free access to EU markets, what date they would stop having free movement of citizens, and just said "everything stops at noon today" then it would be a tiresome muddle.
If a legislation were passed tomorrow saying that the U.K. is officially severing all ties with and exiting from the EU as of, say, the end of 31st July 2016, why shouldn't that be the date for all of those things? British government representatives would make sure they have vacated their EU offices on or before that date, the treasury would stop payments to the EU as of that date, if the U.K. had decided as part of its withdrawal that citizens of certain EU countries were henceforth to need a visa for entry, then immigration at the ports would start enforcing that as of midnight of the 31st July/1st August, and so on.