[susan53]

Hmm ... again yes and no. If you said to me Helen broke off with John, yes I would assume that it was Helen's decision. But if you said Helen broke/split up with John, I don't think I'd assume it was a mutual decision. Rather that the expression doesn't actually explain whose decision it was - it leaves it open. If you've said it in that order, then there's an implication that it was Helen maybe. But it's not so definite as with "broke off". Of course, if you don't know who it was (or don't want to say) then you could always choose an intransitive verb : John and Helen broke/split up. But I still don't think there's any necessary implication that it was mutual. It's just left open.

In fact, I can't think of any expression which definitely implies a mutual agreement. Perhaps because it doesn't happen very often ...