Normally when the switch of ISPs occurs, you lose your broadband connection. You then have to enter your PN details to get connected again. So depending on when the switch occurs (often overnight) and when you notice this will determine how long you are without broadband.
The losing ISP should not cut you off at any time prior to the migration completing. The MAC is valid for 30 days from it being issued so you can plan when the switch actually occurs - i.e near the end of your notice period, to reduce the amount of time you will be paying both ISPs. You can just raise a ticket with PlusNet requesting the date you would like the migration to occur on.
The format of email addresses is
[email protected] where you supply the username when you sign up.