I suppose you could say "Their marriage was on paper only." That means that although they were legally married, they didn't act like husband and wife. They still continued their separate lives.
I agree, but that's not necessarily the same thing as a marriage of convenience. Two British nationals could get married but live separately. They might be doing it for show or for some other strange reason and I would say that theirs is a marriage on paper only.
However, I can't say what I used to do for a living but I can assure everyone that when a foreign national marries a British national purely in order to obtain residency or nationality, it is most certainly called a "marriage of convenience".
I have seen adverts in the back of certain newspapers and magazines, where they are referred to as "mutually beneficial arrangements". In these cases, normally one party receives a fairly substantial sum of money and the other party gets a marriage which could lead to residency/nationality.