Now, Mary was pretty much done for no matter what, but if she didn't stop using her sister's organs, she might take Jodie down as well. That left their parents with three options: 1) Just kinda, you know, chill on the whole thing, letting both twins die in three to six months, 2) separate them right away, letting Mary die but giving Jodie a good chance at a normal life, or 3) separate them only when it was truly necessary, which would more than likely kill Jodie along with Mary. The parents, devout Catholics, chose the "Jesus take the wheel" route, to which their medical team responded, "Wait, 'Let's do nothing' wasn't really an option," and kicked the decision up to the English court system.
There is precedent for this kind of thing. In 1977, a Jewish couple in Philadelphia faced the same conflict. Torn between killing one daughter outright and dooming the other by not doing so, they left the decision up to rabbinical scholars, who determined that separation was permissible because the "weaker" twin was already "designated for death" (also the title of our least favorite Steven Seagal movie).
Jodie and Mary's case worked its way through the courts, ending with the Court of Appeal's decision to proceed with the surgery. Mary passed away the day after the operation, and Jodie has since grown into a healthy teenager who happens to have a hell of a "two truths and a lie" strategy up her sleeve.