The teenager, who is protected by an anonymity order, is left with permanent and serious brain damage. She can only communicate with people who know her well and can only walk a few steps unaided.
Hugh Mercer QC sitting as a Deputy Judge of the High Court paid tribute to the girl's parents who have made significant sacrifices to balance the needs of all the family, including giving up their own careers. As a result of the continuous devotion of the whole family, with the inevitable sacrifices they have made, the girl is a thriving child, the judge said.
The hospital, whose maternity services were heavily criticised for systematic failures, weak leadership and poor quality of care by the Healthcare Commission in 2011, admitted it had breached its duty of care and apologised to the family.
The girl's mother was left on a maternity ward for four days after being induced while midwives failed to notice the baby was in distress. The mother was also given more than the recommended amount of prostin, a drug used to speed up labour.
When the girl was finally born, she had been deprived of oxygen and suffered acute asphyxia. She was floppy and unresponsive and was later diagnosed with cerebral palsy.
The hospital trust admitted that had they delivered her earlier, she would not have been brain damaged.
A spokesman for London North West University Healthcare NHS Trust previously apologies and said that the maternity team has made significant improvements over recent years.
Jane, a specialist birth injury lawyer, said that although the hospital was currently involved in a national programme to increase the safety of mums-to-be and their babies, there was a lot of work to be done nationally to improve people's trust in NHS maternity services following recent scandals at Morecambe Bay and Shrewsbury and Telford.
"That demands proper funding for training and provision of safe levels of staffing in maternity wards, something that is absolutely fundamental to keeping mothers and babies safe."
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