A question of such national import should require a 2/3 majority at least, IMO. Barring that, in the case of a yes vote, a second vote on the exit details should be required. But of course, these requirements would have to have been established prior to the vote. As it stands it is incumbent that the results of the vote, such as it was, be accepted as representing the will of the voters.

Had we gone for a 2/3 majority first time, I would agree with you. But you seem to be saying that if there was a second referendum with say 62% for leave (when that vote is based on current information) that should not overturn on vote of 52% that was several years old (which was based on limited information and lies from both sides.) I would say that is a definite affront to democracy myself.   Having a 2/3 majority for such things make sense, but I don't think you can have different rules for what constitutes a majority for the two referendums.