Up to 20 presents were stolen from a non-public area of the world famous hospital just days before they were due to be distributed among seriously ill youngsters being treated in intensive care.
Scotland Yard condemned the thieves as "disgusting" and "beyond belief" and have appealed for the public's help in catching them.
Now the charity Crimestoppers has offered a reward to anyone who provides information that leads to the identification, arrest and prosecution of those responsible.
The presents, which had been bought from the hospital’s charity fund, included portable DVD players, DVDs and Nintendo DS games consoles.
Earlier this week Metropolitan Police Commissioner Bernard Hogan-Howe urged the public to help catch those responsible.
He told said: "They are ideal gifts for children who aren't very well and are trapped in a hospital at Christmas, yet someone thinks it is a good idea to take them. I would like to make an appeal. If anybody knows where these are - if anybody knows who took them, please tell us."
Devastated staff reported the gifts, believed to have been stored in a cupboard in an area not accessible to the public, stolen yesterday.
Many businesses and organisations offered to replace the gifts.
Detectives believe they were taken sometime between Friday and Monday from the world renowned central London-based hospital, which celebrates its 160th anniversary this year.
Insp Neal Anderson, who is leading the investigation by officers from the Camden borough, described the thieves as callous.
“To steal presents that were supposed to be for children too sick to be at home with their families at Christmas is beyond belief,” he said.
"I would urge anyone who has information about the individual, or persons responsible, to contact officers so that we can try and get the items back before Christmas day.
"I would also urge the thief to try and think about their actions and do the decent thing and return them.”
The hospital, which treats more than 200,000 patients every year, treats some of the most seriously ill young children.
Founded in 1852 by Dr Charles West, it had just ten beds and was the first institution in Britain to offer inpatient care to children only.
Staff and patients, some of whom suffered from life-threatening conditions, played a pivotal role in this year's London 2012 Olympic Games Opening Ceremony as part of a tribute to the hospital.
A hospital spokesman said: "We can confirm there has been a theft and are fully co-operating with the police. We have been overwhelmed by generous offers from individuals and companies to replace the missing items. These items have now been replaced by a long term supporter. Thank you to everyone who has contacted us for their concern and kindness."
No arrests have been made.