'Unbelievably beautiful girl' for Camerons

• British Prime Minister David Cameron and his pregnant wife Samantha pose on the coastal path at Daymer Bay beach during their summer holiday, August 22, 2010 in North Cornwall, England. Samantha Cameron gave birth to a 6lb 1oz baby girl at the Royal Cornwall Hospital in Truro at midday yesterday Picture: Getty

The baby was born weighing 6lb 1oz at the Royal Cornwall Hospital in Truro after Mrs Cameron was rushed to the hospital as a precaution following two days of contractions.

Mrs Cameron, 39, had been due to give birth in September, and arrangements were in place for the Prime Minister to take paternity leave next month.

The birth of the Camerons' fourth child was carried out by Caesarean section, following complications during the birth of their first child Ivan. Last night, both mother and child were said to be well and the Prime Minister told reporters outside the hospital that he would let his wife choose the baby's name, which may have a Cornish connection.

According to bookmakers William Hill, the favourite name is Marnie, followed by Enid, Agnes and Annabel.

The couple who have two other children - Nancy, six, and Arthur, four - had made it clear they wanted another child after the death in February last year of Ivan, who had been severely disabled and needed round-the-clock care.

Speaking on the steps of the hospital, a beaming Mr Cameron said: "We're absolutely thrilled. She is an unbelievably beautiful girl, and I'm a very proud dad and both baby and mum seem to be doing really well, so it's really exciting.

"The other two children are thrilled, bouncing up and down and dying to say hello to the new baby."

He went on: "It's very exciting because we're on holiday and thought that we were going to get through the holiday without having the baby, and it all just sort of kicked off a bit quickly.

"Everything seemed to go fine. We woke up this morning, Samantha woke up this morning, and thought she was having contractions. It was all beginning to get going, so we thought we'd come to the hospital just to get everything checked out. Then things sped up and it all happened very, very quickly, and the baby popped out at about 12 o'clock."

The new baby will be the first in Downing Street since the birth of Tony and Cherie Blair's youngest, Leo, in 2000.

Talking about the birth, Mr Cameron said: "My job was to make the toast and tea and things like that. It's absolutely thrilling, really exciting, and it's just lovely that they're doing so well."

He was full of praise for the NHS staff and the hospital.

"Oh fantastic, it's a wonderful hospital," he said.

"Everyone put us completely at our ease, because it's quite nerve-racking when things happen quickly and they were all absolutely wonderful. So lovely to be here in Truro and to have the baby here."

Mr Cameron admitted the speed of events was a bit of a shock, but was not completely surprised because his wife had tended to give birth early.

Last night, one bookmaker was offering odds of 8/1 of Nick Clegg being made the child's godfather. The Deputy Prime Minister was one of the first to offer his congratulations, along with Labour leadership rivals David and Ed Miliband.

Mr Clegg said: "Miriam and I are absolutely delighted by the fantastic news. All our best wishes are with David and Samantha at this special time for them and their family."

First Minister Alex Salmond said: "Congratulations to David Cameron and his family. It's great news that mother and baby are both doing well."