Apparently Karen is already in a new relationship with an accountant, despite claiming that her marriage is fine. The article was in The Sun, and as much as I loathe the paper, I don't think they'd publish something so defamatory unless they were certain there was some truth in it.
At a guess I'd say that K&K are either in an open marriage which I highly doubt, or more likely have amicably split and just haven't announced it as they wish to continue dancing together.