Sort of, the current occupant would get a message off their own provider saying someone is attempting to take over the line, obviously if they are moving out on the day you move in and it says the migration will take place on that date , why would they be concerned, their service at the address would stop but they wouldn’t be living there, if there were a mistake (the wrong date for example ) they get the option to tell their own provider to stop the migration, in that case your order with BT would be cancelled and you would need to reorder , correcting whatever the problem was that caused the other people to stop it going through….TBH , it sounds as though everything is on track, unless you haven’t picked the correct date, in which case you may be jumping the gun, you would normally do this 10-14 days before the day you take ownership , or ensure the date entered is acceptable to you and them.
