A group of mums and youngsters gathered outside the Mansion House and chanted: "Save Charlie Gard, he's still fighting, we're still fighting" to show their support for the 10-month-old whose parents have lost a legal battle to take him to the USA for experimental treatment.
Charlie's story has even reached the likes of The Pope and American president Donald Trump who have both offered to help.
Chris Gard and Connie Yates had been expecting Charlie's life support to be turned off on Friday after losing a fight against medics who say the tot should be allowed to die with dignity.
London's Great Ormond Street Hospital has been treating Charlie - thought to be one of 16 children in the world to have mitochondrial depletion syndrome.
It is a rare genetic condition which causes progressive muscle weakness and brain damage because he is unable to get energy to his organs.
Doctors have said he now cannot see, hear, move, cry or swallow and has irreversible brain damage. His lungs are only able to keep going because of the treatment he is receiving.
They have argued he should be allowed to die with dignity.
But his parents and supporters have been fighting for him to be given an experimental treatment in the US.
The treatment is not a cure - there isn't one - but it has been suggested it could reduce the effects of the disease.
Judges at the European Court of Human Rights concluded that further treatment would "continue to cause Charlie significant harm", in line with advice from specialists at Great Ormond Street.
President Trump has said he would be "delighted" to help Charlie after his parents lost their legal battle.
A spokeswoman for the White House said President Trump had not spoken to the family although members of the administration had.
"The president is just trying to be helpful if at all possible," she added.