Excerpt from an email...:
"Hangzhou PSB (the police force - ed) told me that if a child born of at least one Chinese parent was born in China, then the child is considered to be Chinese. Though you have registered her birth through the consulate and applied for her British passport, she could not exit from China without going through the following step 1 & step 2 first.
1) Her Chinese Hukou needs to be registered in the Police Station in Gansu where her mother's is located. (that's 2000km away from where we live). The Hangzhou official told me that the details requirements could be very different in different cities.
2) After Francesca’s Hukou is registered, she needs to apply for a single-use Chinese travel document in Gansu PSB to allow her to leave China.
3) After she leaves China and arrives in the UK, she can go to a Chinese embassy and apply for a visa to come to China. "