The Duke and Duchess of Cambridge have welcomed a baby son, with bookmakers tipping Arthur to be the name of the new arrival.

Proud parents William and Kate showed off their third child on the steps of the Lindo Wing private maternity unit, where hundreds of fans and members of the press waited to greet them.

The Duchess gave birth to the 8lb 7oz boy at 11.01am yesterday after being admitted shortly before 6am.

Bookmaker William Hill has been taking bets on the new baby’s name even before he was born, but Arthur has become the odds-on favourite over the last 24 hours.

William Hill spokesman Joe Crilly said: “Arthur has been very well backed over the last 24 hours and the sustained gamble has snowballed, causing the odds to plummet.

“It would not be a surprise if child number three was christened Arthur.”

Arthur is the favourite at 6/4, with Albert and James following behind on 5/1. The bookmaker also lists Phillip

at 6/1.

A formal announcement on the name is expected in the coming days.

During his first photocall, the baby,

a younger brother to Prince George and Princess Charlotte, was wrapped in

a white lace shawl with a matching hat.

Only just under seven hours old, he was carried in his mother’s arms.

Smiling broadly, the Duchess, who was dressed in a vibrant red Jenny Packham dress with a white lace collar, adjusted the baby’s shawl amid windy conditions outside the hospital.

The baby could be seen moving his fingers as he was cradled by Kate.

Minutes after the brief photocall, the couple headed home to Kensington Palace, with William emerging from the hospital carrying his son in a car seat, and holding his wife’s hand.

The Duke said they were “very happy” and “very delighted” and joked, holding up three fingers, that he had “thrice the worry now”.

Questionedd on whether they had decided on a name, the Duke added: “You’ll find out soon enough.”

George and Charlotte earlier met the newest addition to the Cambridge family after being brought to St Mary’s Hospital by Prince William.

A confident Princess Charlotte, who is three on May 2, turned to wave at the photographers as she led the way up the steps holding the Duke’s hand, while four-year-old Prince George appeared more wary of the huge crowds of media.

William and Kate thanked the hospital for their care and the public for their warm wishes.

Kensington Palace said: “Their Royal Highnesses would like to thank all staff at the hospital for the care and treatment they have received.

“They would also like to thank everyone for their warm wishes.”

The new prince is fifth in line to the throne, and the Queen and the Duke of Edinburgh’s sixth great-grandchild.

He is an HRH and a Prince of Cambridge.

By welcoming a baby prince, William and Kate are following in the footsteps of the Queen and Philip.

Kensington Palace announced the baby’s arrival in a statement shortly

after 1pm.