One of each for William and Kate

Royal fans and wellwishers react outside the Lindo Wing of St Mary's Hospital

The arrival of a Princess - the first Windsor baby to use the title for many years - will not just have delighted supporters of monarchy, but the Royal Family as well.

Proud parents the Duke and Duchess of Cambridge will be thrilled to have a daughter.

During her first pregnancy in 2013, Kate told a soldier at a St Patrick’s Day parade in Aldershot, Hampshire, that William was hoping for a girl.

Guardsman Lee Wheeler revealed: “She said ‘I’d like to have a boy and William would like a girl’. That’s always the way.”

Now with a first-born son and a second-born daughter, the Duke and Duchess have one of each.

The baby’s grandfather, the Prince of Wales, will also be overjoyed, having confessed twice that he would like a granddaughter.

Charles, who has two sons and one grandson, Prince George, told a well-wisher after news of the pregnancy was announced: “I’m looking forward to it - but I hope it will be a girl this time.”

The scene outsite the Lindo wing of St Mary's Hospital in Paddington, London

As the Great Kate Wait continued when the Duchess was several days overdue, the Prince again spoke of his wish for a girl.

Meeting veterans and their families on Thursday as the Queen presented new colours to the Welsh Guards at Windsor Castle, Charles chatted to 100-year-old Eric Jones about his hopes.

The centenarian’s daughter, Lynda Bateman, said: ‘’My father introduced me as his daughter and Prince Charles asked how many daughters he had.

‘’My father said ‘One - and that’s enough’ and Charles laughed and said ‘And we’re hoping for a granddaughter!’’’

Prince Harry too was keeping his fingers crossed that William would have a girl.

“I can’t wait to see my brother suffer more,” Harry joked, saying if the second child was a daughter he would “love to see him try and cope with that”.

There were rumours that Kate was expecting a princess amid reports she was experiencing cravings for sweet treats - a sign of a girl, according to an old wives’ tale. She was also said to have ordered several samples of paint in varying shades of pink for Anmer Hall, part of the Sandringham estate in Norfolk.

But the arrival of a girl was a surprise for the couple, who chose not to find out the sex of their baby in advance.

A baby daughter was the firm favourite in the gender betting odds, with punters heavily backing the arrival of a girl.

It has been a quarter of a century since a baby born to the British Royal Family took the title of Princess.

The last - William’s cousin Eugenie - daughter of the Duke of York and Sarah, Duchess of York - was born in 1990.

The Earl and Countess of Wessex’s 11-year-old daughter Lady Louise Mountbatten-Windsor, who was born in 2003, is also technically a princess. As the child of a son of the sovereign, she is entitled to be known as Princess Louise.

But Edward and Sophie decided, with the Queen’s agreement, that their daughter would use the courtesy title of the child of an earl instead.

Although Kate uses the title Duchess, she is technically a princess as well - Princess William of Wales - through her marriage to William. She cited her job as “Princess of the United Kingdom” on George’s birth certificate.

This is the first time a great-granddaughter of a still-serving sovereign has been born in direct succession on the male line since 1897, when George VI’s sister Princess Mary was born.

The baby is also the first Princess of Cambridge to be born for 182 years. The last was King George III’s granddaughter, Princess Mary Adelaide of Cambridge, who was born in Hanover, Germany, in 1833.