Royal baby: The prince meets his people in world media frenzy

Prince William says he and the Duchess are 'still working on a name' and their son has spent his first night at his Kensington Palace home

It was the moment the whole world had been waiting for. With a joke about the new baby having more hair than his father, the Duke and Duchess of Cambridge presented their newborn son to the waiting press at the front of St Mary's Hospital.

The royal couple posed for the pictures, waving and smiling at the cheering well wishers from the steps of the Lindo Wing.

The Duchess held her son first and the couple looked relaxed and smiled broadly as the world's media captured the moment.

William later held his son and walked forward with his wife to answer a few questions, before joking: "He's got a good pair of lungs on him, that's for sure. He's a big boy, he's quite heavy."

The baby prince was the star attraction and appeared oblivious to the flashguns of the world's press photographers going off, but did seem to be partially awake during his first public appearance, as his hand poked over the white shawl he was wrapped in.

Asked how he felt, William replied, "very emotional". "It's such a special time and I think any parent will probably know what this feeling feels like," he said.

The Duchess of Cambridge holds her newborn son, the third in line to the throne (Getty) (Getty Images)

William and Kate's appearance outside the Lindo Wing harked back to the day the Duke first emerged into the world outside the same hospital in the arms of the Prince and Princess of Wales in 1982.

The new royal baby - the first Prince of Cambridge to be born for more than 190 years - was delivered yesterday at 4.24pm, weighing 8lb 6oz.

His parents have yet to name their son and the Duke said it was now a priority: "We're still working on a name so we will have that as soon as we can."

The couple later emerged with their son in a baby seat and William carefully fitted it onto the backseat of a Range Rover beside his wife before driving his family home.

The Queen tonight revealed she was "thrilled" at the arrival of her first great-grandson.

In the hours before they left hospital William and Kate had received visits from their son's grandparents Michael and Carole Middleton and the Prince of Wales and Duchess of Cornwall.

Charles's visit to the hospital was an historic moment as it is believed to be the first time three male heirs to the throne - Charles, his son William and grandson - who are expected to reign, have come together in more than a hundred years.

The last time a similar gathering happened was likely to have been before Queen Victoria's death in 1901 when her son, later Edward VII, was with his son the future George V and grandson, later Edward VIII.

Asked how his first grandchild was, Charles replied: "Marvellous, thank you very much, absolutely wonderful."

Prince Charles and Camilla leave The Lindo Wing after visiting The Duke and Duchess Of Cambridge and their newborn son at St Mary's. (Getty Images)

Mr and Ms Middleton then spent just over an hour with the Duke and Duchess at the Lindo Wing.

Mrs Middleton described her grandson as "absolutely beautiful" as she left the hospital and, speaking about mother and baby, said: "They are both doing really well, and we are so thrilled."

But when asked if she had suggested a name for the baby, she said: "Absolutely not, but thank you."

Their visit came after the King's Troop Royal Horse Artillery and Honourable Artillery Company made their way to Buckingham Palace to carry out the ceremonial royal salutes in honour of the new addition to the Royal Family.

Carole and Michael Middleton, the parents of the Duchess of Cambridge, arrive at St. Mary's hospital to visit their daughter and her newborn baby boy (EPA)

Gun salutes are fired for the birth of every prince or princess, no matter where their place is in the line of succession, according to the Ministry of Defence.

The King's Troop Royal Horse Artillery, wearing full dress uniform, rode past Buckingham Palace to Green Park where they staged a 41-gun royal salute. 71 horses pulled six First World War-era 13-pounder field guns into position for the royal salute at 2pm.

Each of the six guns fired blank artillery rounds at 10-second intervals until 41 shots were fired. The Honourable Royal Horse Artillery fired a 62-gun salute from the Tower of London at the same time.

A full peal of bells have also began at Westminister Abbey, and will last for three hours.

There were celebrations across Britain and messages of congratulations were sent from leading figures across the world. Twitter descended into a royal baby frenzy when, at its peak, 25,000 tweets a minute were sent discussing his arrival.

The Duchess stayed overnight at the Private Lindo wing of St Mary's Hospital with Prince William and their son. They released a joint statement thanking staff at the hospital on Tuesday. Their statement said: “We would like to thank the staff at the Lindo Wing and the whole hospital for the tremendous care the three of us have received. We know it has been a very busy period for the hospital and we would like to thank everyone - staff, patients and visitors - for their understanding during this time.”

Crowds of people try to look at a notice formally announcing the birth of a son to the Duke and Duchess of Cambridge, placed in the forecourt of Buckingham Palace (Reuters)

William's uncle Earl Spencer described his joy at the new royal baby, saying: “We're all so pleased - it's wonderful news."

Earl Spencer, whose sister was the Duke's mother, Diana, Princess of Wales, added: “My father always told us how Diana was born on just such a blisteringly hot day, at Sandringham, in July 1961. It's another very happy summer's day, half a century on.”

Yesterday evening, Trafalgar Square was illuminated in blue to mark the child's gender while the BT Tower was lit up with the message: 'It's a boy!'

The BT tower shows a message saying "It's a Boy" following the announcement that the Duchess of Cambridge has given birth to a baby boy (Rex Features)

The British Monarchy's Twitter account announced the music being played during a special Changing of the Guard in a tweet: "Today's Changing the Guard music at #BuckinghamPalace will include 'Congratulations' 'Royal Salute' and 'The Duke of Cambridge March'."

London's Natural History Museum, of which Kate is patron, is celebrating the birth of the new prince by lighting up its main Waterhouse building blue at sunset every night for three nights.

Michael Dixon, Director of the museum, said: “Following the announcement earlier this year that the Duchess has chosen to be the patron for the Natural History Museum, we are overjoyed to receive news of the royal birth.

Additional reporting by PA