Britain has erupted in wild celebration as the newest addition to the royal family begins to take visitors and speculation as to what the newly-born prince will be called heats up.

Prince William and Kate Middleton welcomed their third child Monday night and the expanded family is getting used to the new addition at home at Kensington Palace after briefly showing him off to the world.

Kate’s younger sister Pippa Middleton, who is herself reportedly expecting her first child with husband James Matthews, arrived at Kensington Palace to meet her new nephew on Wednesday morning (AEST).

Wearing a pink coat and an oversized pink turtleneck, Middleton was one of the first family members to meet the newborn.

William’s cousin Princess Eugenie also arrived for a visit, while Prince Charles will meet his grandson after returning from Anzac Day centenary commemorations in France.

William’s bother Prince Harry and fiancèe Meghan Markle, are also expected to be one of the first to meet the new prince.

The much-anticipated birth was marked by bell ringing at Westminster Abbey, a 41-round gun salute in London’s Hyde Park and a 62-round salute at the Tower of London.

The newest royal is getting used to his new family at home. Photo: Getty

With the new prince’s name expected to be revealed at any moment, punters are racing to place bets on the possible name of the new royal baby boy.

James and Henry are catching up to favourite Arthur in the betting stakes.

“Arthur might be the favourite with the bookies, but it’s actually James that’s the favourite with punters,” Jessica Bridge of bookmakers Ladbrokes said.

William Hill spokesman Rupert Adams said: “Henry has been very popular overnight and might well be in the frame”.

Coral spokesman Harry Aitkenhead said: “Arthur is the hot favourite at the moment and ever since the birth yesterday our customers have been queuing up to get their bets on.

“James, Albert and Philip have also been backed and anything else would be a major shock.”

The birth of the new prince was marked across Britain. Photo: EPA

Charles has spoken of his delight at the birth of his latest grandchild, joking “the only trouble is I don’t know how I am going to keep up with them”.

He said the arrival of the new royal baby was a “great joy”.

The heir to the throne, who turns 70 this year, is also grandfather to Prince George and Princess Charlotte.

“We are both so pleased at the news,” Charles 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.”

-with AAP