not on = not right or fair - not acceptable won't put up with it = I wont suffer it - I wont allow it to keep happening

In my opinion, "This is just not on" means that something what you say is not on that point, "I wont put up with it" means that I wont bear it or cannot stand it anymore

"This is just not on" means that the situation is not correct or just.

Hi - I would just like to add that "This is just not on" sounds quite awkward to me. Nick could be right in his interpretation but it is hard to be sure without some context.

I guess what was on Nick's mind was - to be fed up sth - I'm fed up with your loud music! To put up with is rather to tolerate (eg sb's bad behaviour), manage, deal wit sth - Better put up with her behaviour instead of starting another bust-up.