David Cameron led the congratulations to the Duke and Duchess of Cambridge on the birth their new daughter. 

"I'm absolutely delighted for them," the Prime Minister declared on his Twitter feed.

Deputy Prime Minister Nick Clegg said that he and his wife Miriam wished them "all the best as their family grows".

"This is great news and an exciting time not only for them, but also Prince George," he said.

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

Labour leader Ed Miliband tweeted: "Congratulations to the Duke and Duchess on the birth of their daughter. Wishing them lots of joy and happiness - and hopefully some sleep!"

Meanwhile, Mr Clegg revealed he was invited into a voter's house to watch the announcement on TV.

The Lib Dem leader tweeted: "On the doorstep in Sheffield. Thanks to the kind constituents who invited me in to see the great royal baby news being announced on their TV".

Ukip leader Nigel Farage said the birth of the royal baby was an "exciting and joyous event for millions of patriotic British people".

"I strongly urge all Ukip candidates to take at least an hour out of campaigning in order to toast the new arrival. I shall certainly be setting an example in that regard. After all, some things are worth interrupting politics for," he said.

Mr Farage said he was happy the baby's weight was announced in imperial measurements.

He said: "Imperial measurements, proper measurements - eight pounds three ounces.

"Not some horrid kilogramme measurement, I'm very, very pleased. Perhaps that tells us where the royal family really stand."

During a visit to Hastings, Mr Miliband said: "I would like to congratulate the Duke and Duchess of Cambridge on the fantastic news.

"I know the whole country will be wishing them incredibly well.

"I know as a father who went through anxious moments at the birth of my two kids that it is an anxious time, but now will be a joyous time for them both."

The Archbishop of Canterbury, the Most Revd Justin Welby, said: "It's wonderful news that the Duke and Duchess of Cambridge have a healthy new baby girl.

"Like many here and abroad, I'm delighted for the royal couple on this special day. May God bless them and both of their children with love, health and joy."

A host of celebrities have joined the world in congratulating the Duke and Duchess of Cambridge on the birth of their baby princess.

Singer and former X Factor judge Cheryl Fernandez-Versini tweeted: "Congratulations William and Kate. So excited to see our new little princess!!"

TV host Jonathan Ross tweeted: "Royal baby yay! Makes me happy. Republicans need not respond."

Singer and TV star Peter Andre wrote: "Congratulations to the Duke and Duchess of Cambridge on their baby daughter. Great great news."

Olympic gold medallist and swimmer Rebecca Adlington wrote: "Awwww its a girl!!!!! How exciting!! Congratulations Will and Kate!"

Bishop of Durham the Right Rev Paul Butler said: "Anybody who has been a parent or grandparent will know something of the joy and anxiety that the birth of a new baby brings. On behalf of the congregations of the Diocese of Durham, I send our warmest congratulations to the Duke and Duchess on the birth of their daughter."

Celebrations were in full swing outside the Lindo Wing as royal fans sang: "Princess! Princess! Princess!"

After several days of camping outside, dedicated royalists were singing and dancing with joy at the news that the Duchess of Cambridge has given birth.

Terry Hutt, who celebrated his 80th birthday this week and is from Weston-super-Mare, said: "I'm on top of the world."

He said he did not expect the birth to happen as soon as it did, but said: "Babies come when they're ready."

Mr Hutt added: "If Diana was here, she'd be very, very proud."

Mr Hutt said he is happy the baby is a girl "because she's going to make more babies for us".

As a group of excited teenagers stood nearby chanting "Princess! Princess! Princess!", royal camper Sky London, 54, said: "I feel over the moon."

Jacquie Knighton, 56, said: "What a lovely child she's going to be."

As the crowds shouted "hip hip hooray", camper Damian Andrews, 42, said: "I'm so excited. Now they've got a boy and a girl and hopefully they'll use Diana's name as one of the names."

Kathy Martin, 52, originally from Australia, jumped up on a wooden bench and held aloft a banner that said "It's a princess" while fellow camper John Loughrey, 60, danced in the centre of a crowd surrounded by camera crews and photographers.

Well-wishers arrived at the gates of Kensington Palace, the official residence of the Duke and Duchess of Cambridge, to hand over flowers to congratulate the couple on their new baby.

Holly, 12, and Katy, nine, from Balham in south London, handed in a bunch of pink, purple, orange and yellow gerberas to a police officer manning the palace gates.

Their mother Natalie Trumper said: "Apparently we are the first people to have given a bunch of flowers to the palace this morning.

"We have been to the hospital but couldn't get very close and we have been very excited about the imminent arrival of the new baby.

"We have been hoping she would have a girl, and all our hopes came true this morning when the news was announced.

"We aren't that sure about some of the names being suggested though - we want Eliza rather than Alice.

"It was too good an opportunity to miss coming here, with it being the weekend."

Katy said: "I'm excited to see the new baby."

There was a celebratory atmosphere in Cafe Diana, located across the road from Kensington Palace, where the Duke and Duchess of Cambridge live.

Managers let off pink and union jack balloons and handed out lemon cake to their customers to mark the arrival of the couple's baby girl.

The cafe, which opened in 1989, is named after Diana, Princess of Wales and covered in photographs of the royal.

Cafe owner Abdul Daoud, 59 brought in a life-sized cardboard cut-out of the Duke and Duchess of Cambridge as he released the balloons.

He said: "It's a special day. Prince William came here with his mum many years ago when he was at school and lived with his mum.

"The cafe was named after Princess Diana and when we opened she came and congratulated us and supported us. She was very fond of the cafe.

"I hope Prince William and Kate will come and visit us one day."