The Siamese twin girls, joined from the breastbone to the naval, were born on November 26 in London and underwent an 11-hour operation on December 2 to separate them. The girls shared a liver, but had separate hearts. Hope died during surgery as her lungs were too small to sustain her.
"We were always clear that Faith was very sick," the hospital spokesman said.
"She required the full range of skills of our intensive care staff, and underwent a number of further procedures. However, she succumbed to the complexities of her condition," the spokesman told BBC.
Faith had undergone surgery earlier this month to correct circulatory problems so that more blood would flow through her body and not through her lungs, according to the spokesman.
The twins were delivered via a caesarian section to Laura Williams, 18. She is believed to be the youngest mother in Britain to give birth to Siamese twins. Both parents were by Faith's side when she died in the hospital.
On average, one in four patients die during or after separating conjoined twins. Even if one of the twins dies, the operation is considered successful. There is always a risk of organ shutdown during this type of surgery.
The term "Siamese twins" comes from the previous name of Thailand, Siam, the birthplace of the first known conjoined twins, Chang and Eng Bunker, who were born in 1811. They later moved to the United States, married two sisters, fathered 10 and 11 children each, shared two households (three days with each wife), and died one hour apart on the same day in 1874.