A High Court in London approved the settlement amount of around £39m after the child, who cannot be identified, was taken to Frimley Park Hospital in Surrey with "red flags for meningitis and sepsis", lawyers said.

After being discharged and given paracetamol for symptoms including a high temperature and drowsiness, lawyers said that it wasn't until she was taken back to A&E with a rash and a fever, that she was diagnosed with meningococcal sepsis.

The young girl was transferred to another hospital where she suffered from multi-organ failure and subsequently had above-knee amputations of both of her legs and above-elbow amputations of her arms.

She also underwent several other procedures, including skin grafts, to treat the infection.

The Frimley Health NHS Foundation Trust admitted liability after the family brought a claim against it, arguing that the child would have avoided amputations and would not have been so ill, if she had been treated urgently with antibiotics.

Judge Caspar Glyn KC "unhesitatingly" approved the settlement, which will be paid partly in a lump sum and the rest in annual payments for the rest of her life.

The case was described as "very sad" by the family's senior barrister, Elizabeth-Anne Gumbel KC, who added that the child has significant scarring over her body.

"She is an extraordinarily brave little girl who is managing in school to do very well academically," Ms Gumbel said.

In a letter addressed to the child's parents, Frimley Health NHS Foundation Trust chief executive Neil Dardis, apologised, adding that her care "fell below the standard (that she) was entitled to expect" and that she should not have been discharged.

Bradley Martin KC, representing the trust, added: "There is no amount of money that can truly compensate (her) for her injuries.

"She will have access to the care and technology she needs. It is quite remarkable that despite such devastating injuries, she has such potential."