This is what the left-wing Guardian reported -
A new prime minister must be designated, that will take a few days, he said, adding that it would not be respectful to delay the process.
I think Boris is really saying that a new govt. needs to be installed in Westminister since they will be the negotiating team. Since the process takes two years minimum a few more months won't make much difference and changing negotiators in mid-stream is never good.
Boris is being very naive if he truly believes that delaying Article 50 is a good idea.
Delay too long and the the “stay” camp (which Cameron is a part of) will find a way to invalidate the vote. Cameron is mostly stalling at this point and hoping that the 4 month delay will be painful enough to change the outcome.