I don't have recent experience of this (my present package has not resulted in my exceeding my usage limit, for years), but isn't it the case that "add-on" blocks are sold in units of 2 GB? So the "duplicate" e-mails might simply be a reflection of the fact the overuse was two lots of 2, or 4.
I'm afraid I can't help you as to how the overuse may have come about, or even if it
did come about. Barring a metering error by Plusnet, it does appear that the most likely explanation is someone else using your wireless connection.
I do take it there are not other people in the house, who might have used the connection without your knowledge? A friend once caught her cleaning-lady doing this, when she was supposed to be working at cleaning the house!