A simple mix-up in an operating theatre that left a "happy, active" 10-year-old girl with catastrophic brain damage has led to the NHS facing a £24m payout – the largest in a case of medical negligence.

Maisha Najeeb was keen on dancing and hoped to become a doctor when glue was accidentally injected into her brain during surgery at Great Ormond Street children's hospital in London in June 2010.

The accident occurred when a syringe containing glue was mistaken for one containing dye. Maisha, who is now 13, suffered what her lawyers describe as "catastrophic and permanent brain damage". She is in a wheelchair, can barely move, is blind in one eye, needs round the clock care and suffers from painful spasms in her legs.

In a settlement agreed at the high court in London, she will receive an initial £2.8m plus annual payments of £383,000 until she is 19. That will then rise to £423,000 a year until she dies.

If she lives until she is 64, as an expert hired by her family said they expected, then the NHS would have to eventually pay total damages of almost £24.2m.

"We are sad and devastated by what happened to our daughter. Her life is ruined. All her dreams have been broken," said Maisha's father, Sadir Hussain. He said he hoped that the family's legal action meant that "lessons will have been learned to avoid this happening to other families".

The hospital, which admitted liability, offered "unreserved apologies for the shortcomings in her care, the consequences of which have been tragic and devastating for Maisha and her family." It could not say if any member of staff had been disciplined over the incident. After an internal inquiry, the hospital has established an action plan of improvements, including the introduction of full colour-coding for all fluids and medications used in radiology procedures and, crucially, a new system of labelling syringes. Maisha's family had "engaged open-heartedly" with them and helped with that overhaul, said a hospital spokesperson.

The NHS Litigation Authority, which insures hospitals against lawsuits for medical negligence and acts on their behalf, will pay the agreed damages rather than Great Ormond Street itself.

Edwina Rawson, the family's solicitor at Field Fisher Waterhouse, said: "What is so heartbreaking about this case is that the injury was so avoidable.If the syringes had been marked up so the hospital could see which contained glue and which contained dye, then Maisha would not have suffered what is an utterly devastating brain injury. Such easily avoidable mistakes should not happen."

Before the blunder Maisha was a healthy 10-year-old, though she suffered from a rare condition called arterio-venous malformation (AVM), in which arteries and veins become tangled, which can lead to bleeding. Each time she suffered a bleed she went into Great Ormond Street for embolisation, in which glue is used to seal off the blood vessels that are bleeding and dye to highlight the blood flow.

The two sides could not agree on what impact the brain damage and AVM would have on Maisha's life expectancy. Her family said she could live until she was 64, but the hospital estimated that she could die of a bleed on her brain by 23.

Deborah Evans, chief executive of the Association of Personal Injury Laweyers, said the money would pay for the 24/7 care that Maisha will need forever. "While this is possibly the largest agreed payment we have seen, the amount is dependent on life expectancy and will never replace the life she would have led," Evans said.