New Royal baby girl introduced to the world

She made her first public appearance around nine hours later - fast asleep - when the Duke and Duchess briefly posed on the steps of St Mary's Hospital, London, with their new arrival, before travelling home to Kensington Palace.

Earlier Prince William, who was at his wife's side during the delivery, had told the crowds of well-wishers and assembled media he was "very happy" as he left in the afternoon to pick up Prince George, who was brought back to the hospital for a short time to meet his new sister.

Kate - who is known as the Countess of Strathearn in Scotland - was a number of days overdue and had been taken to the Lindo wing of St Mary's Hospital at 6am from Kensington Palace.

The announcement of the birth was a mix of the traditional and modern. An official notice was placed at Buckingham Palace - an age-old custom - and town crier Tony Appleton stood on the steps on the Lindo wing to announce the news.

However a series of tweets from the official Kensington Palace account also announced the safe arrival of the baby girl, her weight and that "Her Royal Highness and the child are both doing well."

Thousands of well-wishers gathered outside St Mary's Hospital after the announcement of the birth in the hope of catching a first glimpse of the new Royal, who will be known as the Princess of Cambridge.

The crowd included dedicated royalists who had spent several days camping outside in anticipation of the birth. Terry Hutt, from Weston-super-Mare, who celebrated his 80th birthday this week, said: "I'm on top of the world."

Tower Bridge was also lit up in pink in celebration of the news - although this did provoke some criticism of sexism. "Are we really still in the 1950s with gender norms?" asked one Twitter user.

The birth will also be commemorated by the Royal Mail with a special postmark on letters delivered on Tuesday which reads: "Congratulations TRH The Duke and Duchess of Cambridge on the birth of their daughter." It is the first time in the company's 500-year history a Royal birth has been marked in this way.

The Duchess was looked after by consultant obstetrician Guy Thorpe-Beeston, who is the surgeon-gynaecologist to the royal household. He was joined in the delivery room by Alan Farthing, the Queen's surgeon-gynaecologist. A suite at the private wing in St Mary's Hospital costs upwards of £6,570 for a one-night stay with "normal delivery".

Bookies have estimated they face a payout of more than £500,000 after heavy backing for a princess rather than a prince.

Alice is the favourite contender for the name of the new Princess of Cambridge, which was the name of the Duke of Edinburgh's mother and a daughter of Queen Victoria. Other bookie's favourites include Charlotte, Victoria and Elizabeth.

The Duchess of Cambridge's daughter is the Queen's fifth great-grandchild. The birth comes as the Queen prepares to overtake her ancestor Queen Victoria as the longest reigning British monarch in history this September.

Politicians took time out from the last few days of election campaigning to offer their congratulations. Prime Minister David Cameron posted on Twitter feed: "I'm absolutely delighted for them."

First Minister Nicola Sturgeon said she was "delighted" at the news and offered her "warmest congratulations" to the royal couple.

In a radio interview Mayor of London Boris Johnson couldn't resist an election reference saying: "I suggested to a certain amount of apathy that she should be called Victoria in honour of the coming Conservative victory.... What will she be called? Who knows? Coalitia? Let's hope not."

But posts on Twitter showed not everyone was joining in the celebrations of the birth. One user wrote: "What have these Royals done to be Royalty or even deserve for us to care? #RoyalBaby #thisis2015 #AbolishTheMonarchy".

Another Tweet said: "I'm sure people will be celebrating as they head down to the food banks to feed their own poverty stricken children."