Tell the truth. However, going to and fro all the time like that is bound to cause difficulties with immigration at the airports on both sides. If you want to be together long term, get working on how you plan to do that - who is moving where and on what kind of visa. Definitely DO NOT pretend she is still married to her ex, that could cause all kinds of problems if she ever applied for a fiance or marriage visa to come and live in the UK.
Best of luck to you, it's not easy.