The Duke and Duchess of Cambridge returned home to spend the first night with their new baby daughter, after leaving the hospital to cheers from fans.

William and Kate showed off their baby daughter to the world's press as they left St Mary's Hospital in London on Saturday, just 10 hours after the princess's birth.

Prince William, who had been at Kate Middleton's side during the birth, told the press he was "very happy".

The name of their second child is not yet known, although it may be revealed later on today.

The royal couple announced the name of their first child Prince George the day after they left the hospital in July 2013.

TheCambridges are expected to stay at Kensington Palace for the next fewdays,before they depart for their retreat in the country, Anmer Hall in Norfolk on the Queen's Sandringham estate.

Members of the Royal Family and the duchess's parents may also visit.

#Royalbaby arriving home #FrontRowSeats ??

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The princess is fourth in line to the throne and was born at 8.34am on Saturday 2 May, weighing 8lbs 3oz.

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."

Trafalgar Square's fountains and the London Eye were also illuminated on Saturday night, while Tower Bridge was lit up in pink to mark the birth.

Tourism bosses are predicting the birth of the new princess will bring even more visitors to London than the arrival of Prince George.

VisitLondon said that London will have nearly 32 million UK and overseas tourists this year – well up on the 29.1 million total achieved in 2013 – the year Prince George was born.