LONDON — When Zainab Bibi gave birth to her eighth and ninth children — twin girls — it was five days before she was well enough to be introduced to them. All she knew was that they had both survived the cesarean section and were healthy.

At the hospital in Peshawar, Pakistan, she was given a photograph to prepare her for the discovery to come: The girls were conjoined at the skull. Surgery to separate them, she was later told, would almost certainly end one of the girls’ lives.

“They were very beautiful and they had nice hair with white skin,” Ms. Bibi told the BBC. “I didn’t even think about the fact they were joined. They are God-given.”

The thought of losing one of them was unfathomable.

That was in the winter of 2017. A potential solution appeared three months later, when the family was introduced to Noor ul Owase Jeelani, a neurosurgeon at Great Ormond Street Hospital in London, where teams of specialists have successfully treated two similar cases since 2006.