Trafalgar Square’s fountains and the London Eye were also illuminated on Saturday night to mark the birth.
The Cambridges will spend the next few days at Kensington Palace; afterwards they are expected to travel to their country home Anmer Hall on the Queen’s Sandringham estate in Norfolk.
Bookmakers have said Charlotte and Alice have emerged as the favourite names for the princess, followed by Olivia, Victoria and Elizabeth.
A spokeswoman for Ladbrokes said: “We’ve never known a day of royal speculation like it. Charlotte is the new favourite, but Olivia is the name on the nation’s lips.”
Meanwhile, almost all of the UK’s national newspapers have given over the entire front pages of their Sunday editions to the birth and a photograph of the new princess.