Boys and girls from Hill House School raised £2,013.67 for the appeal at their end of term mufti day.
They gave a cheque to the appeal at their school assembly on 29 June.
Laura Watts, head of community and events fundraising, said: “We would like to say a huge thank you to Hill House School for all their support.
“The money they have raised will make a huge difference to our appeal and will help the children’s intensive care unit at St Mary’s Hospital to save even more lives.”
Every year, around 400 patients are cared for in the children’s intensive care unit at St Mary’s but it also turns away hundreds more critically ill children because it does not have enough beds. This means children may have to be transferred hundreds of miles for treatment.
Last year, the unit had to turn away 233 children, more than half the number actually admitted.
The More Smiles Appeal, led by Imperial College Healthcare Charity and COSMIC, aims to create a new unit with 15 beds, almost doubling the current number, allowing more than 200 extra children to be cared for each year.
There will also be new equipment, a dedicated parents' room and a private room allowing space for doctors and nurses to provide emotional support and care to families whose children are very seriously ill.