Baby kept you up, Wills? Prince looks unshaven following his first night as a father-of-three after auntie Pippa and Eugenie become first visitors to see Kate and the new royal arrival

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The Duke of Cambridge today left Kensington Palace one day after his wife Kate gave birth to their third child.

Prince William appeared to be unshaven and looked tired this afternoon as he and the Duchess of Cambridge settle into life as a family of five after bringing their new baby son home to West London from hospital yesterday.

Pregnant Pippa Middleton today visited her new royal nephew, with Kate's 34-year-old sister seen leaving the palace this afternoon after spending two hours with the newborn baby, who is fifth-in-line to the throne.

Pippa, 34, smiled broadly through her car window, wearing a baby pink coat, pink turtleneck and brown tortoiseshell sunglasses. Her visit came before gun salutes were fired in Hyde Park and Tower Bridge to mark the birth.

Princess Eugenie of York arrived just before 6pm in a chauffeured car, wearing a turquoise patterned blouse, to welcome her first cousin once removed into the family.

She is due to wed Jack Brooksbank after seven years together on October 12 in St George's Chapel at Windsor Castle - the same location as Prince Harry and Meghan Markle. 

The date of the wedding falls on a Friday - breaking with royal tradition of holding marriage ceremonies on the weekend. 

Prince William leaves Kensington Palace in London by car this afternoon, hours after his wife Kate gave birth for the third time

New father the Duke of Cambridge is pictured driving out of Kensington Palace the day after the birth of the new royal baby

Pippa Middleton leaves Kensington Palace in London today after visiting her newborn nephew

The 34-year-old smiled broadly for photographers through the window of her car today

Pippa was wearing a baby pink coat, pink turtleneck and brown tortoiseshell sunglasses

Prince Charles, who will soon visit his new grandson, said today: 'We are both so pleased at the news. 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.'

The Prince of Wales will visit his grandson after returning from Anzac Day centenary commemorations of the Battle of Villers-Bretonneux in France on April 25, 1918, to which he is travelling today.

Meanwhile William and Kate's closest relatives are being kept in the dark over the new name, with the Countess of Wessex saying today: 'The jury's out on that one. I don't know, we're all just going to have to wait and see!'  

The always-charming Sophie, who is married to William's uncle Prince Edward, and was on a visit to Tregolls School in Truro, Cornwall, told MailOnline: 'I'm thrilled for them all, it's lovely - really good news.'

Pippa herself is expecting her first child, with she and her 42-year-old financier husband James Matthews due to become parents in the autumn.

The mother-to-be is taking bespoke diet and exercise classes from the £8,000-a-year KX gym in Kensington to lead her successfully through her first pregnancy.

The happy news is no doubt hugely welcome after a difficult few weeks for the family following allegations of rape against her father-in-law David Matthews.

He has called the claims 'untrue and scandalous'. The 74-year-old allegedly carried out two offences between 1998 and 1999, one in Paris and another in St Barts.

Eugenie arrived in a chauffeured car at Kensington Palace to visit her first cousin once removed today

A 62-gun salute was fired outside the Tower of London this afternoon to mark the birth of the royal baby

The salute was carried out by the King's Troop Royal Horse Artillery and the Honourable Artillery Company

The 41-gun salute was held in Hyde Park at the same time as 62 rounds were fired near the Tower of London (pictured)

Members of the Honourable Artillery Company fire a 62-gun salute from the Tower of London to welcome the birth today

Members of the King's Troop Royal Horse Artillery fire a 41 gun salute from Hyde Park to welcome the birth of the child

The 41-gun salute from Hyde Park today welcomed the birth of the Duke and Duchess of Cambridge's third child

Members of the King's Troop Royal Horse Artillery arrive to fire the 41-gun salute from Hyde Park this afternoon

Kate was said to have been the first person to be told of Pippa's pregnancy after James Matthews. The couple married in May last year.

The Duke and Duchess of Cambridge post with their newborn son yesterday outside the Lindo Wing at St Mary's Hospital in Paddington, London

Today, Prince William and Kate are settling into life as a family of five after bringing their new baby son home from St Mary's Hospital in Paddington

Kensington Palace said the name would be announced in 'due course' but the favourite at the bookies is currently Arthur, followed by James, Philip and Albert

Prince George and Princess Charlotte, who visited their new sibling at St Mary's Hospital in Paddington, London, yesterday, are likely to be at school and nursery today

Prince William and his wife spent their first night as a family of five at their home in West London after their new baby son was born at about 11am yesterday.

Kensington Palace said the name would be announced in 'due course' but the favourite at the bookies is currently Arthur, followed by James, Philip and Albert.

More than 100,000 bets have now been put on the baby name, with James the most popular in terms of individual wagers placed with bookmaker Ladbrokes.

Big bets placed with the company yesterday included £11,000 for the baby to be a boy at 10/11, as well as £2,000 on Philip and £1,000 on both James and Albert.

The Duke and Duchess of Cambridge pose with their newborn son yesterday outside the Lindo Wing at St Mary's Hospital in Paddington, London

Prince William joked yesterday, holding up three fingers, that he had 'thrice the worry now'

More than 100,000 bets have now been put on the baby name, with James the most popular in terms of individual wagers placed with one bookmaker

Today, while the public continue to try to guess the name, the Army will fire gun salutes at Hyde Park and the Tower of London at 2pm in honour of the new arrival.

The baby prince's great-grandmother the Queen, 92, is still at Windsor Castle for Easter Court, with the Duke of Edinburgh who is recovering after a hip operation.

Prince George and Princess Charlotte, who visited their new sibling at St Mary's Hospital in Paddington, London, yesterday, are likely to be at school and nursery. 

William and Kate have retreated to the sanctuary of Kensington Palace after introducing their third child to the world on the steps of the Lindo Wing at St Mary's. 

Prince Charles, pictured at the Queen's Birthday Party at the Royal Albert Hall on Saturday, today told of his 'great joy' at the Duke and Duchess of Cambridge 's newborn son

The Duke and Duchess thanked the hospital for their care and the public for their wishes

During his first photocall, the baby, who was wrapped in a white lace shawl with a matching bonnet, could be seen moving his fingers as he was cradled by Kate

The London Eye is illuminated in red, white and blue yesterday to show support for the Duke and Duchess of Cambridge after they welcomed their new baby son into the world

The name of the 8lb 7oz baby prince of Cambridge has yet to be unveiled. Royals traditionally keep the public guessing before revealing their choice.

William and Kate will want to share the name with the Queen and the rest of their family before making it public - but it is likely to be revealed by the end of tomorrow.

A confident Charlotte, who turns three on May 2, turned to wave at photographers outside the hospital as she led the way up the steps holding William's hand.

Four-year-old George, in his school uniform from Thomas's Battersea, appeared more wary of the huge crowds of media.

During his first photocall, the baby, who was wrapped in a white lace shawl with a matching bonnet, could be seen moving his fingers as he was cradled by Kate.

Prince George and Princess Charlotte visited their new sibling at St Mary's Hospital yessterday

A confident Charlotte turned to wave at photographers outside the hospital as she led the way

Smiling broadly, the Duchess was dressed in a vibrant red Jenny Packham dress with a white lace collar, reminiscent of William's late mother Diana, Princess of Wales.

She wore red and white outside the Lindo Wing after Prince Harry was born in 1984.

As William and Kate headed home after appearing in front of the cameras with their seven-hour-old son, the Duke said they were 'very happy' and 'very delighted'.

He joked, holding up three fingers, that he had 'thrice the worry now', adding: 'We didn't keep you waiting too long this time.'

Quizzed on whether they had decided on a name, the Duke added: 'You'll find out soon enough.' The Duke and Duchess thanked the hospital for their care and the public for their 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 words 'It's a boy' flashed in lights around the top of London's BT Tower yesterday, while the London Eye was illuminated in red, white and blue yesterday to show support for the family. 

By welcoming a baby prince, William and Kate are following the birth pattern of the Queen and Philip's children - a son, a daughter and then another son.

The Queen and the Duke had Prince Charles, then Princess Anne, then Prince Andrew after a ten-year gap, with a fourth child, Prince Edward, born four years later.