Not many babies experience so much fanfare on their first day in the world — but the new royal is preparing for a highly unusual life.

Today, the little prince received visitors including Pippa Middleton and Princess Eugenie, as his tired-looking father Prince William was seen driving out of Kensington Palace while mum Kate stayed at home with the kids.

The birth was marked by bell-ringing at Westminster Abbey, a 41-round gun salute in London's Hyde Park at 2pm Tuesday local time and a 62-round salute at the Tower of London.

Pippa was among the little prince's first visitors, looking cheerful as she drove into the palace in a baby-pink turtleneck, coat and sunglasses. Kate Middleton's 34-year-old sister is expecting her first child with her hedge fund manager husband James Matthews.

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Princess Eugenie arrived to visit her cousin William's new baby just before 6pm in a chauffeured car, wearing a blue print top. Prince Charles will visit his grandson after returning from Anzac Day centenary commemorations in France.

The Prince of Wales on Tuesday said: "It is a great joy to have another grandchild, the only trouble is I don't know how I am going to keep up with them."

When William eventually takes over the title, if Prince Charles ascends the throne as expected, the new baby will also be Prince X of Wales.

The newborn Prince of Cambridge is as yet unnamed, and speculation over the possible name is reaching fever pitch. Although he was born on St George's Day, his 4-year-old brother is already named after the patron saint of England.

Arthur is now the favourite with the bookmakers. Ladbrokes is putting the name at 5/2, James at 4/1, Albert at 5/1, Philip at 6/1 and Alexander at 10/1. Traditional royal names Frederick, Henry, Edward, Michael and Thomas are also in the running.

His Royal Highness spent his first full day in the world surrounded by family and friends, as the world waits with bated breath to learn more about him.

Meanwhile, lip-readers told the Mirror what Kate and her husband murmured to each other as they posed with their third child for his first photographs.

"Are you okay with him?" the Duke of Cambridge, 35, asked the Duchess as she walked down the hospital steps in stilettos, just hours after the birth.

"Yes," the confident 36-year-old replied.

They then prompted each other to wave in different directions, before Kate told her spouse: "It is a bit windy, he might get cold, let's go now."

The youngest member of the monarchy was born in the private Lindo Wing of St Mary's Hospital in central London, with a crowd of hundreds waiting outside. Some had been camped outside the hospital for two weeks.

The little boy's parents William and Kate are one of the most famous and influential couples in the world, but would have seemed like any other doting mother and father to the newborn, who arrived safely on Monday morning UK time.

The royal machine soon swung into gear, as the Duke of Cambridge braved the cameras to bring the prince's older brother and sister — Prince George of Cambridge and Princess Charlotte of Cambridge — to meet him and see his mother, the Duchess.

Within seven hours of the prince's birth at 11.01am local time, his mum was glammed up by a professional stylist and slipped into nude heels and a shift dress for his first taste of the cameras. She wore a red dress with white collar by British designer Jenny Packham, believed to be a tribute to the prince's late grandmother Princess Diana.

Swaddled in a white lace shawl, the 3.8kg baby had no knowledge of the extraordinary excitement and delight at his birth sweeping the world as the shutters clicked for his first newspaper front pages.

"We didn't keep you waiting too long this time," said his beaming father William telling the media he and Kate were "very happy" and "delighted", but adding that they had "thrice the worry now" as he held up three fingers.

As for the baby's name, he told the press, "You'll find out sooner or later".

The couple then headed back inside the hospital before placing their son's car seat in the royal Range Rover and taking him home to Kensington Palace to join George and Charlotte.

The little prince is fifth in line to the throne, bumping his uncle Prince Harry from the spot but not usurping his older sister, for the first time in history after the Succession to the Crown Act was passed in 2013, ending male primogeniture in the royal family for those born after 2011.

Charlotte and George's names were announced within a day or two of their births respectively, although William's took a week and his father Charles's name wasn't revealed for a month.

The wider royal family is also thrilled at the news. Kensington Palace yesterday said: "The Queen, The Duke of Edinburgh, The Prince of Wales, The Duchess of Cornwall, Prince Harry and members of both families have been informed and are delighted with the news."

The pomp and circumstance began with a notice announcing the birth placed in the forecourt of Buckingham Palace, a large Union Jack raised over the palace and a State Standard over Windsor Castle to mark the occasion.

The Duke and Duchess of Cambridge thanked the staff at the hospital for the care they received and "everyone for their warm wishes".