If they couldn't take him home, they wanted to keep him alive on a respirator in a hospice facility so they could have several more days together.
Great Ormond Street bosses said they were not satisfied that a properly-qualified specialist would be in control under Charlie's parents' plan.
The 11-month-old baby suffered from an extremely rare genetic condition causing progressive brain damage and muscle weakness, and his parents' long struggle to save him drew an global outpouring of sympathy, including from US President Donald Trump and Pope Francis.
On Monday Gard and Yates abandoned a five-month legal battle and withdrew a petition to take him to the USA, after concluding he had deteriorated "to the point of no return". It's not enough to know what the parents want; Charlie has to come first in the law.
Described as "perfectly healthy" when he was born, Charlie was admitted to hospital at eight weeks and his condition has progressively deteriorated.
Fard suffered from a rare genetic disease, mitochondrial depletion syndrome. It causes progressive muscle weakness and brain damage. "His parents'? Or are sick babies - and others facing futile-care impositions - ultimately owned by the hospital and the state?"
The case resurfaced a decades-old debate over euthanasia and the use of life support, issues that have been fought in most corners of the world and that have often seen medical and religious arguments collide. He tweeted his support and then the White House telephoned Prof Hirano and requested he call Great Ormond Street. By this point his breathing is shallow and he is lethargic.
The American doctor who offered the treatment flew to Britain to examine Charlie and determined the therapy would fail.
Doctors at the hospital, which specialises in paediatric care, said that the youngster should be taken off life support, which was only prolonging his suffering. The parents kept fighting, showing a remarkable tenacity just as Charlie was showing in remaining alive.
It was to give them a final chance of making such an arrangement that the judge gave them until noon on Thursday.
When they realized that Charlie's condition was beyond treatment, they simply wanted him to die in their arms in a private hospice after they could spend a few final days saying goodbye.
2 July: Demonstrators gather outside Buckingham Palace to protest against the decision to allow Charlie's treatment to be withdrawn.
Charlie Gard has died after his life support is switched off, his family have reportedly said.
The case caught the attention of Donald Trump and Pope Francis after the European Court of Human Rights refused to intervene. The pediatric hospital Bambino Gesù in Rome, known as "the pope's hospital", offered to care for the boy. Both said an experimental treatment known as nucleoside therapy had a chance of helping Charlie.